When A 40 kg child is riding a 20 kg bike down the road then The child has more momentum than the bike. hence option B is correct.
Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s. Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum. The dimensions of the momentum is [M¹ L¹ T⁻¹].
Hence momentum is mass times velocity. In this problem child and bike is going with same velocity hence mass defines the greatness of the momentum. the child has greater mass than the bike, hence child has greater momentum.
Hence option B is correct.
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A negatively charged rod is brought close to an uncharged electroscope. While the rod is close one's finger touches the far side of the metal ball on the electroscope. After the charged rod has been removed the finger is removed. The electroscope is
When a negatively charged rod is brought close to an uncharged electroscope and one's finger touches the far side of the metal ball on the electroscope, the electroscope becomes positively charged.
Here's the step-by-step explanation:
1. A negatively charged rod is brought close to the metal ball of the uncharged electroscope. This induces a charge separation in the electroscope due to the influence of the rod's electric field. The electrons in the electroscope are repelled by the negatively charged rod, leaving the metal ball with a net positive charge.
2. While the negatively charged rod is still close to the electroscope, one's finger touches the far side of the metal ball. This provides a grounding path for the excess electrons in the electroscope to move through, leaving the electroscope with a net positive charge.
3. After the charged rod has been removed, the electric field influence of the rod is no longer present. However, the electroscope remains positively charged as the excess electrons have already left through the grounding path.
4. Finally, the finger is removed, leaving the electroscope in a positively charged state.
In conclusion, after following these steps, the electroscope is left positively charged.
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T/F Negative work means you are performing work in the negative direction
Negative work simply means that the work done is in the opposite direction to the force applied, regardless of the direction of the force.
False. Negative work does not necessarily mean that work is being done in the negative direction.
Work is defined as the product of force and displacement, with the direction of the force and displacement determining the sign of the work. If the force and displacement are in the same direction, then the work done is positive. If the force and displacement are in opposite directions, then the work done is negative.
However, the sign of the work does not necessarily correspond to a direction. For example, if a force is applied to an object in the upward direction, but the object moves downward, the work done by the force is negative, even though the force was applied in the positive direction. Similarly, if a force is applied in the negative direction, but the object moves in the positive direction, the work done by the force is positive.
Therefore, negative work simply means that the work done is in the opposite direction to the force applied, regardless of the direction of the force.
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Compare and contrast frequency-dependent wave summation with motor unit recruitment (previously observed by increasing the stimulus voltage). How are they similar? How was each achieved in the experiment? Explain how each is achieved in vivo.
Frequency-dependent wave summation and motor unit recruitment are both processes by which an increase in a stimulus can lead to an increase in muscle contraction.
What is stimulus?Stimulus is a term used to describe any kind of external influence that can cause a change in behavior or thought. It is a broad term that can refer to a range of different events or stimuli, from physical objects to psychological stimuli. Stimulus can be either positive or negative, and can either cause an increase or decrease in behavior.
Frequency-dependent wave summation and motor unit recruitment are both processes by which an increase in a stimulus can lead to an increase in muscle contraction.
Frequency-dependent wave summation was achieved in the experiment by applying repetitive electrical stimulation to a muscle at increasing frequencies. The stimulation would cause a wave of depolarization to run through the muscle, resulting in a contraction. As the frequency of the stimulation increased, the strength of the contraction increased due to the summation of the waves.
Motor unit recruitment was achieved in the experiment by increasing the voltage of the stimulation. This would cause a stronger depolarization of the muscle and result in a stronger contraction. As the voltage of the stimulation was increased, the number of motor units recruited to contract the muscle would also increase.
In vivo, frequency-dependent wave summation is achieved by the nervous system sending signals to the muscle at increasing frequencies. This causes a wave of depolarization to run through the muscle, resulting in a stronger contraction.
In vivo, motor unit recruitment is achieved by the nervous system sending signals to the muscle at increasing voltage. This causes a stronger depolarization of the muscle, resulting in a stronger contraction. As the voltage of the signal increases, the number of motor units recruited to contract the muscle also increases.
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The gravitational force between two objects of mass M and 2M respectfully, is measured to be F when the two are placed a distance R from each other. If the distance is increased to 2R what would be the new force between the objects?
The new force between two objects of mass M and 2M is measured to be F when the two are placed a distance R from each other and the distance is increased to 2R would be one-fourth of the original force, or F/4.
The new gravitational force between two objects of mass M and 2M when the distance is increased from R to 2R can be calculated using the formula:
F_new = (G × M × 2M) / (2R)²
Where F_new is the new force, G is the gravitational constant, M is the mass of the first object, 2M is the mass of the second object, and 2R is the new distance between them.
Since the initial force F = (G × M × 2M) / R², we can substitute this into the equation:
F_new = F / 2²
F_new = F / 4
So, when the distance between the objects is increased to 2R, the new gravitational force between them will be one-fourth of the original force, or F/4.
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Two satellites of the same mass are placed in orbits around Earth. Satellite A is at an altitude of RE and Satellite B at an altitude of 2RE where RE = 6.38x10^6 m and is the radius of Earth. What is the ratio of the potential energy of Satellite B to Satellite A?
The ratio of the potential energy of Satellite B to Satellite A is 2/3. This means that Satellite B has about 67% of the potential energy of Satellite A.
To calculate the ratio of the potential energy of Satellite B to Satellite A, we need to use the formula for gravitational potential energy:
U = [tex]- G (m_1m_2)/r[/tex]
where U is the gravitational potential energy, G is the gravitational constant ([tex]6.67 \times 10^{-11}\: Nm^2/kg^2[/tex]), [tex]m_1[/tex] and [tex]m_2[/tex] are the masses of the two satellites, and r is the distance between them.
Since both satellites have the same mass, we can simplify the formula to:
U = [tex]- G m^2 / r[/tex]
where m is the mass of each satellite.
The distance between the center of Earth and Satellite A is RE, so the distance between Satellite A and Earth's center is (RE + RE) = 2RE. Similarly, the distance between the center of Earth and Satellite B is (2RE + RE) = 3RE.
So, the ratio of the potential energy of Satellite B to Satellite A is:
[tex]U_B / U_A = (- G m^2 / 3RE) / (- G m^2 / 2RE)[/tex]
Simplifying this expression, we get:
[tex]U_B / U_A = 2/3[/tex]
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suppose you observe a star orbiting the galactic center at a speed of 1400 km/s in a circular orbit with a radius of 20 light-days. calculate the mass of the object that the star is orbiting.
The mass of the object that the star is orbiting around the galactic center is approximately 2.13 × 10^12 kg.
To calculate the mass of the object that the star is orbiting around the galactic center, we can use the following formula derived from Newton's law of gravitation and centripetal force:
M = (v^2 * R) / G
where M is the mass of the object, v is the orbital speed of the star (1400 km/s), R is the orbital radius (20 light-days), and G is the gravitational constant (approx. 6.674 × 10^-20 km^3/kg s^2).
First, we need to convert the orbital radius from light-days to kilometers. One light-day is approximately 25,902,068,371.2 km. Therefore, 20 light-days is equal to:
20 * 25,902,068,371.2 km = 518,041,367,424 km
Now we can substitute the values into the formula:
M = ((1400 km/s)^2 * 518,041,367,424 km) / (6.674 × 10^-20 km^3/kg s^2)
M ≈ 2.13 × 10^12 kg
So the mass of the object that the star is orbiting around the galactic center is approximately 2.13 × 10^12 kg.
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a block of mass 10 kg is pulled to the right along a rough horizontal surface with a constant horizontal force of 20 n. the friction force is known to have a magmitude 5 n. what is the net force on the block? choose the positive direction to be to the right.
If a a block of mass 10 kg is pulled to the right along a rough horizontal surface with a constant horizontal force of 20 n. the friction force is known to have a magnitude 5 n.The net force on the 10 kg block is 15 N to the right.
To find the net force on the block follow these steps:
1. Identify the forces acting on the block: The horizontal force (20 N) is acting to the right, while the friction force (5 N) is acting to the left (opposite direction).
2. Choose the positive direction: In this case, the positive direction is to the right.
3. Calculate the net force: Net force = Horizontal force - Friction force. Since the horizontal force is in the positive direction and the friction force is in the opposite direction, the calculation becomes: Net force = 20 N - 5 N = 15 N.
The net force on the 10 kg block is 15 N to the right.
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In SHM, the speed of the block reaches its maximum value when the block is ...
a. in the equilibrium position.
b. at either its rightmost or leftmost position.
d. between its rightmost position and the equilibrium position.
d. between its leftmost position and the equilibrium position.
At the equilibrium position, the acceleration of the block is zero, and therefore, the velocity is at its maximum value. The correct answer is a. in the equilibrium position.
The speed of the block decreases as it moves away from the equilibrium position and reaches zero at the rightmost or leftmost position before changing direction and starting to move back towards the equilibrium position.
In Simple Harmonic Motion (SHM), the speed of the block reaches its maximum value when the block is:
a. in the equilibrium position.
The reason for this is that when the block is at its rightmost or leftmost positions, its speed is momentarily zero before changing direction. As the block moves towards the equilibrium position, its speed increases, reaching its maximum value at the equilibrium position. From there, as the block continues moving towards the opposite extreme, its speed decreases until it reaches zero again at the rightmost or leftmost position.
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A 0.20-kg object is oscillating on a spring with a spring constant of k = 15 N/m. What is the potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude?
The potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude, is 0.024 J.
When an object is oscillating on a spring, it has both kinetic and potential energy. The potential energy of the system is stored in the spring and is a function of the displacement of the object from its equilibrium position. In this case, the object has a mass of 0.20 kg and is oscillating on a spring with a spring constant of k = 15 N/m.
To calculate the potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude, we first need to determine the amplitude of the oscillation. The amplitude is the maximum displacement from the equilibrium position, and in this case, it is twice the displacement of 0.040 m, or 0.080 m.
The potential energy of the system is given by the formula U = 1/2 [tex]kx^2[/tex], where k is the spring constant and x is the displacement from the equilibrium position. Plugging in the values, we get:
U = 1/2 (15 N/m) [tex](0.040 m)^2[/tex]
U = 0.024 J
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an ideal gas with molecules of mass m iscontained in a cube with sides of area a. thepressure exerted by the gas on the top of the cubeis p, and n molecules hit the top of the cube in atime dt . what is the average vertical componentof the velocity of the gas molecules?
The average vertical component of the velocity of the gas molecules can be calculated using the kinetic theory of gases.
According to the kinetic theory of gases, the average kinetic energy of a gas molecule is directly proportional to the temperature of the gas:
KE = (1/2)mv^2 = (3/2)kT
where m is the mass of the molecule, v is the velocity of the molecule, k is the Boltzmann constant, and T is the temperature of the gas.
The pressure exerted by the gas on the top of the cube can be related to the average kinetic energy of the gas molecules:
p = (n/A) * (m/A) * v^2/3
where n/A is the number of molecules hitting the top of the cube per unit time, and (m/A) is the mass of each molecule per unit area.
Solving for v, we get:
v = sqrt(3p/m) * sqrt(A/n)
The average vertical component of the velocity can be obtained by multiplying v by the cosine of the angle between the velocity vector and the vertical axis, which is equal to 1/sqrt(3). Therefore, the average vertical component of the velocity of the gas molecules is:
vz = v * 1/sqrt(3)
vz = sqrt(3p/m) * (1/sqrt(3)) * sqrt(A/n)
vz = sqrt(p/m) * sqrt(A/n)
Hence, the average vertical component of the velocity of the gas molecules is proportional to the square root of the pressure and the area, and inversely proportional to the square root of the number of molecules hitting the top of the cube per unit time and the mass of each molecule.
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a certain superconducting magnet in the form of a long solenoid of length 0.500 m can generate a magnetic field of 9.00 t in its core when its coils carry a current of 75.0 a. find the number of turns in the solenoid.
The number of turns in the solenoid is 10.08 x 10⁴.
Length of the solenoid, L = 0.5 m
Magnetic field, B = 9 T
Current flowing through the solenoid, I = 75 A
The magnetic field due to a current carrying solenoid,
B = μ₀NI/L
Therefore, the number of turns,
N = BL/μ₀I
N = (9 x 0.5)/(4[tex]\pi[/tex] x 10⁻⁷x 75)
N = 10.08 x 10⁴
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which of the drawings in the figure best illustrates what happens when the temperature of a helium-filled rubber balloon is increased at constant pressure?
The figure that best illustrates is: look for the drawing that shows an increase in the balloon's volume when the temperature is increased, while the pressure remains constant.
To determine which drawing in the figure best illustrates what happens when the temperature of a helium-filled rubber balloon is increased at constant pressure, you should consider the relationship between temperature and volume in a gas system.
When the temperature of a helium-filled rubber balloon is increased at constant pressure, the gas molecules in the balloon gain energy and move faster. This causes the gas to expand, increasing the volume of the balloon. This behavior can be explained by Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure is held constant.
So, search for the illustration in the picture that depicts a rise in the balloon's volume as the temperature rises while the pressure stays the same.
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could someone please help I dont understand :(
I answered the first question but im not sure its right
The pair of objects on the left feel a much greater force than the pair on the right because the charges on the left are of opposite polarity, while the charges on the right are of the same polarity.
What is polarity ?Polarity is a measure of the direction of a magnetic field or electric field. It is a fundamental property of the universe and is found in many physical phenomena, including the behavior of charged particles and the electromagnetic force. In a magnetic field, the direction of the field lines is referred to as the polarity of the field. In an electric field, it is the direction of the electric field vector that determines the polarity. In both cases, a positive polarity indicates a field pointing away from the source, while a negative polarity indicates a field pointing toward the source.
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T/F Force A has a moment arm of 20cm and a magnitude of 5 N. Force B has a moment arm of 5cm and a magnitude of 20 N. The system of forces is in static equilibrium
Force A has a moment arm of 20 cm and a magnitude of 5 N, and Force B has a moment arm of 5 cm and a magnitude of 20 N. The system of forces is in static equilibrium.
In order for a system to be in static equilibrium, the sum of the torques (moments) acting on the system must be equal to zero. Let's calculate the torques produced by Force A and Force B:
1. Convert the moment arms to meters:
Moment arm of Force A = 20 cm = 0.2 m
Moment arm of Force B = 5 cm = 0.05 m
2. Calculate the torque produced by each force:
Torque of Force A = Moment arm of Force A × Magnitude of Force A = 0.2 m × 5 N = 1 Nm
Torque of Force B = Moment arm of Force B × Magnitude of Force B = 0.05 m × 20 N = 1 Nm
3. Check if the system is in static equilibrium:
Since the torques produced by Force A and Force B are equal and opposite (assuming they act in opposite directions), their sum is zero:
Torque of Force A + Torque of Force B = 1 Nm - 1 Nm = 0 Nm
Thus, the system of forces is indeed in static equilibrium.
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What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 ´ 103 kg/m3 and water density = 1.0 ´ 103 kg/m3)
The cylinder displaces 0.0007407 cubic meters of water.
How to find the volume of water?The volume of water displaced by a submerged object is equal to the volume of the object.
The volume of the aluminum cylinder can be calculated using its density and mass:
Volume of cylinder = Mass of cylinder / Density of aluminumVolume of cylinder = 2.0 kg / (2.7 × 10³ kg/m³)Volume of cylinder = 0.0007407 m³Since the volume of water displaced by the cylinder is equal to the volume of the cylinder, we can conclude that the cylinder displaces 0.0007407 cubic meters (or 740.7 milliliters) of water.
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After a pendulum starts swinging, its amplitude gradually decreases with time because of friction. What happens to the period of the pendulum during this time?
The effect of friction on the amplitude of the pendulum does not affect the period of the pendulum, but it does affect the accuracy and speed of the pendulum.
The period of a pendulum refers to the time it takes for the pendulum to complete one swing, i.e., the time it takes for it to move from one end to the other and back again. The period of a pendulum is determined by the length of the pendulum and the force of gravity, and it is not affected by the amplitude or the mass of the pendulum.
Therefore, even though the amplitude of the pendulum gradually decreases due to friction, the period remains constant as long as the length and force of gravity do not change. This means that the time it takes for the pendulum to complete one swing remains the same regardless of the amplitude of the pendulum.
However, it is important to note that the amplitude of the pendulum does affect the maximum speed of the pendulum during each swing. As the amplitude decreases, so does the maximum speed of the pendulum, which means that the pendulum takes longer to complete each swing. Additionally, as the amplitude decreases, the pendulum becomes less accurate in keeping time, and the period may vary slightly over time.
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A glider with a spring attached to each end oscillates with a certain period. If identical springs are added in parallel to the original glider, what will happen to the period?
The new period of oscillation will be 2π√(m/((n + 1)k)).
When identical springs are added in parallel to the original glider, the effective spring constant of the system increases. This is because the springs are now acting together to produce a greater force, and thus the restoring force on the glider is greater than before.
As a result, the period of the oscillation will decrease. The period of oscillation for a mass-spring system is given by:
T = 2π√(m/k)
Where T is the period, m is the mass of the glider, and k is the spring constant. Since the mass of the glider does not change when additional springs are added in parallel, the period will decrease due to the increase in the effective spring constant (k_eff).
The effective spring constant of the system with n identical springs in parallel is given by:
k_eff = (n + 1)k
Therefore, the new period of oscillation will be:
T' = 2π√(m/(k_eff))
= 2π√(m/((n + 1)k))
Since k_eff > k, T' < T, which means that the period of oscillation will decrease when identical springs are added in parallel to the original glider.
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Fixing the brakes on your bicycle, you have the bicycle turned upside down. To test the brakes, you spin the wheel to a high speed in a clockwise direction from your perspective. As you apply the brakes and wheel is slowing, what is the direction of the angular acceleration?
Means that the wheel's rotational speed will decrease as it slows down due to the braking force.
When you apply the brakes to a rotating bicycle wheel, friction is created between the brake pads and the wheel rim. This frictional force acts in the opposite direction to the direction of the wheel's motion, which in this case is clockwise when viewed from your perspective.
According to Newton's Second Law, the angular acceleration (α) of a rotating object is directly proportional to the net torque (τ) acting on the object and inversely proportional to its moment of inertia (I). The direction of the angular acceleration is in the same direction as the net torque.
In this case, the net torque acting on the wheel is in the counterclockwise direction, which is opposite to the clockwise direction of the wheel's motion. Therefore, the direction of the angular acceleration is also counterclockwise. This means that the wheel's rotational speed will decrease as it slows down due to the braking force.
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Suppose that you have a 570 −Ω , a 950 −Ω , and a 1.2 −kΩ resistor.
What is the maximum resistance you can obtain by combining these?
The maximum resistance you can obtain by combining 570 −Ω , a 950 −Ω , and a 1.2 −kΩ resistors is 2,720Ω.
To find the maximum resistance you can obtain by combining a 570Ω, a 950Ω, and a 1.2kΩ resistor, you should connect them in series. In a series connection, the total resistance is the sum of the individual resistances. Here's a step-by-step explanation:
1. Convert the 1.2kΩ resistor to Ω: 1.2kΩ = 1,200Ω
2. Connect the resistors in series: R_total = R1 + R2 + R3
3. Add the resistance values: R_total = 570Ω + 950Ω + 1,200Ω
4. Calculate the total resistance: R_total = 2,720Ω
The maximum resistance you can obtain by combining these resistors is 2,720Ω.
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a texas cockroach of mass 0.i7 kg runs counterclockwise around the rim of a lazy susan (a circular disk mounted on a vertical axle) that has radius 15 cm, rotational inertia 5.0 x 10-: kg 'm2, and frictionless bearings. the cockroach's speed (relative to the ground) is 2.0 m/s, and the lazy susan turns clockwise with angular velocity o)0 : 2.8 rad/s. the cockroach finds a bread crumb on the rim and, of course? stops. (a) what is the angular speed of the lazy susan after the cockroach stops? (b) is mechanical energy conserved as it stops?
(a) The angular speed of the lazy susan after the cockroach stops is 2.20 rad/s.
(b) The mechanical energy of the system is not conserved as the cockroach stops
How to find angular speed?(a) To solve for the angular speed of the lazy susan after the cockroach stops, we can use the conservation of angular momentum, which states that the total angular momentum of a system is conserved in the absence of external torques. Initially, the angular momentum of the system (lazy susan and cockroach) is:
L_i = I * w_i + m * r * v
where I is the rotational inertia of the lazy susan, w_i is its initial angular velocity, m is the mass of the cockroach, r is the radius of the lazy susan, and v is the velocity of the cockroach relative to the ground.
Since the cockroach is running counterclockwise and the lazy susan is turning clockwise, their angular momenta have opposite signs, so we can use the convention that counterclockwise angular momenta are positive and clockwise ones are negative. Thus, the initial angular momentum of the system is:
L_i = - I * w_i + m * r * v
Substituting the given values, we get:
L_i = - (5.0 x 10⁻³ kgm²) * (2.8 rad/s) + (0.17 kg) * (0.15 m) * (2.0 m/s)
L_i = -0.0196 kgm²/s
When the cockroach stops, its velocity becomes zero, so the angular momentum of the system is conserved and becomes:
L_f = I * w_f
where w_f is the final angular velocity of the lazy susan. Equating the initial and final angular momenta, we get:
L_i = L_f
(5.0 x 10⁻³ kgm²) * (2.8 rad/s) + (0.17 kg) * (0.15 m) * (2.0 m/s) = (5.0 x 10⁻³ kgm²) * w_f
Solving for w_f, we get:
w_f = 2.20 rad/s
Therefore, the angular speed of the lazy susan after the cockroach stops is 2.20 rad/s.
How to determine mechanical energy conserved as it stops?(b) To determine whether mechanical energy is conserved as the cockroach stops, we can calculate the initial and final kinetic energies of the system. Initially, the kinetic energy of the system is:
K_i = (1/2) * I * w_i² + (1/2) * m * v²
Substituting the given values, we get:
K_i = (1/2) * (5.0 x 10⁻³ kg*m²) * (2.8 rad/s)² + (1/2) * (0.17 kg) * (2.0 m/s)²
K_i = 0.155 J
When the cockroach stops, its kinetic energy becomes zero, so the final kinetic energy of the system is:
K_f = (1/2) * I * w_f²
Substituting the calculated value of w_f, we get:
K_f = (1/2) * (5.0 x 10⁻³ kg*m²) * (2.20 rad/s)²
K_f = 0.027 J
Therefore, the mechanical energy of the system is not conserved as the cockroach stops, since there is a decrease in kinetic energy from 0.155 J to 0.027 J.
This decrease in kinetic energy is due to the work done by the frictional force between the cockroach and the lazy susan, which causes the cockroach to stop.
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a travel bag has a carrying capacity of 9 kg . if clothes weighing 4.5 kg and food items weighing 3.7 kg are put into it, how much more weight can it carry?
Answer:
The answer is 0.8kg
Explanation:
Total mass =9kg
mass of object 1=4.5kg
mass of object 2=3.7kg
Tm=m1+m2+x
9=4.5+3.7+x
9=8.2+x
x=9-8.2
x=0.8kg
assuming that the air is still, how long would it take a large raindrop (5 mm diameter) to reach the ground if it fell from a cloud base at 3000 meters? how long would a typical raindrop (2 mm) take to fall to the ground from the same cloud? how long if it were a drizzle drop (0.5 mm)?
A typical raindrop would take 500 seconds
How long would a typical raindrop (2 mm) take to fall to the ground from the same cloud?
To calculate the time it takes for a raindrop to fall to the ground, we can use the formula: time = distance / speed. The terminal velocities for different raindrop sizes are approximately:
- Large raindrop (5 mm): 9 m/s
- Typical raindrop (2 mm): 6 m/s
- Drizzle drop (0.5 mm): 2 m/s
Assuming the cloud base is at 3000 meters, we can calculate the time for each type of raindrop as follows:
Large raindrop (5 mm): time = 3000m / 9 m/s = 333.33 seconds
Typical raindrop (2 mm): time = 3000m / 6 m/s = 500 seconds
Drizzle drop (0.5 mm): time = 3000m / 2 m/s = 1500 seconds
So, a large raindrop would take about 333.33 seconds to reach the ground,A normal raindrop takes 500 seconds to form., and a drizzle drop would take 1500 seconds to fall from the cloud base at 3000 meters to the ground when the air is still.
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(A)Heat flow(B)Kinetic energy(C)Potential energy(D)First law of thermodynamics(E)Second law of thermodynamicsThe amount of energy in an isolated system stays constant.ABCDE
A road bike has tires that have a diameter of 0.800m and is rolling down the road at 20.0m/s. What is the angular velocity of the bike tire?
The angular velocity of the bike tire is 50 radians per second.
To find the angular velocity of the bike tire, we can use the formula:
ω = v / r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the tire.
In this case, we are given the diameter of the tire, which is 0.800m. To find the radius, we need to divide the diameter by 2:
r = 0.800m / 2
r = 0.400m
We are also given the linear velocity of the bike, which is 20.0m/s. Plugging these values into the formula, we get:
ω = 20.0m/s / 0.400m
ω = 50.0 rad/s
Therefore, the angular velocity of the bike tire is 50.0 rad/s.
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Suppose a flute and an oboe alternately play A4 (440 Hz) tones. The difference in tone color between the instruments can be observed by comparing which aspect of their sounds?
The difference in tone color between a flute and an oboe when they alternately play A4 (440 Hz) tones, the difference can be observed by comparing the timbre of their sounds.
Timbre refers to the unique quality or character of a sound, which is influenced by the instrument's construction and the manner in which it produces sound. Tone color is another term for timbre, and it helps us differentiate between the sounds of various instruments even when they are playing the same pitch and at the same volume.
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A steel railroad track has a length of 34 m
when the temperature is −3◦C.
What is the increase in the length of the
rail on a hot day when the temperature is
30 ◦C? The linear expansion coefficient of
steel is 11 × 10−6(◦C)−1
.
Answer in units of m.
The increase in the length of the rail on a hot day when the temperature is 30 °C is 0.0363 m.
What is length?Length is a measurement of distance or size. It is one of three fundamental measurements (along with width and height) used to describe the size of an object. Length can be measured in a variety of units, such as meters, feet, inches, or centimeters. In mathematics, length is defined as the longest dimension of an object or distance between two points. In physics, length is a fundamental quantity used to measure objects and distances.
The increase in the length of the rail on a hot day when the temperature is 30 °C can be calculated using the formula for linear expansion:
ΔL = L0 * α * ΔT
Where L0 is the original length of the rail (34 m), α is the linear expansion coefficient of steel (11 x 10-6 (°C)-1), and ΔT is the change in temperature (30 °C - (-3 °C) = 33 °C).
Plugging in the values, we get:
ΔL = 34 m * 11 x 10-6 (°C)-1 * 33 °C
ΔL = 0.0363 m
Therefore, the increase in the length of the rail on a hot day when the temperature is 30 °C is 0.0363 m.
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Question 1-22: During the time that the temperature remained constant, what do you think happened to the heat energy you were transferring if it wasn't raising the temperature?
During the time that the temperature remained constant, the heat energy you were transferring was not raising the temperature because it was being used for a phase change. In other words, the heat energy was being absorbed to change the state of the substance (e.g., from solid to liquid or liquid to gas) without increasing its temperature. Once the phase change is complete, any additional heat energy transferred to the substance will cause its temperature to rise again.
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In the nuclear reaction given by 14,7N + 4,2He = n,mX + 1,1H, what is the nucleus n,mX?
The nucleus n,mX is 17,8X. Based on the atomic number (m = 8), the element is oxygen. Therefore, the nucleus is 17,8O (oxygen-17). The nuclear reaction is 14,7N + 4,2He = 17,8O + 1,1H.
In the given nuclear reaction:
14,7N (nitrogen-14) + 4,2He (helium-4) = n,mX + 1,1H (hydrogen-1)
First, let's analyze the conservation of mass and atomic numbers in the nuclear reaction. To do this, we add the mass numbers (the top numbers) and the atomic numbers (the bottom numbers) on each side of the equation.
Mass numbers:
14 (N) + 4 (He) = n (X) + 1 (H)
18 = n + 1
Atomic numbers:
7 (N) + 2 (He) = m (X) + 1 (H)
9 = m + 1
Now, we can solve for n and m:
n = 18 - 1 = 17
m = 9 - 1 = 8
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How does slice thickness artifact commonly express itself ?
a. a fill-in of cystic structures
b. improper brightness of reflectors
c. absence of reflectors
d. strong linear echoes
Slice thickness artifact commonly expresses itself as: d. strong linear echoes .
When slice thickness artifact occurs, it commonly expresses itself as strong linear echoes on the ultrasound image. This is because the ultrasound beam is not able to accurately focus on the entire thickness of the structure being imaged, resulting in multiple echoes being received from the different layers within the structure. These echoes can appear as strong, parallel lines on the image and can lead to misinterpretation of the anatomy being imaged.
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A car traveling down the road at 25.0 m/s has a wheel spinning at 45.0 rad/s. A deer jumps in front of the car causing the driver to slam on the brakes and slow to 10.0 rad/s in 1.75 s. What is the angular acceleration of the car?
The negative sign indicates that the angular acceleration is in the opposite direction to the initial angular velocity (i.e., it is slowing down).
We can use the following formula to calculate angular acceleration:
α = (ωf - ωi) / t
where
ωi = initial angular velocity
ωf = final angular velocity
t = time interval
Here, the initial angular velocity ωi = 45.0 rad/s and the final angular velocity ωf = 10.0 rad/s, and the time interval t = 1.75 s.
Plugging in these values, we get:
α = (10.0 rad/s - 45.0 rad/s) / 1.75 s
α = -25.7 rad/s^2
The negative sign indicates that the angular acceleration is in the opposite direction to the initial angular velocity (i.e., it is slowing down).
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