Answer:
The time taken before the phone hits the ground is 1.4 s.
Explanation:
Given;
height of the rock wall, h = 10 m
speed of the climber, v = 0.25 m/s
The time taken before the phone hits the ground is given;
h = ut + ¹/₂gt²
10 = 0.25t + ¹/₂(9.8)t²
20 = 0.5t + 9.8t²
9.8t² + 0.5t - 20 = 0
solving this quadratic equation;
t = 1.4 s
Therefore, the time taken before the phone hits the ground is 1.4 s.
A student made a model of an onion skin cell she viewed using a microscope. The scale is 500:1. The student's cell model has a length of 15 cm. How many centimeters is the cells length
I feel like I'm in a city
Answer:
0.03 cm
Explanation: If the scale is 500:1, you have to divide 500 by 15 to get 0.03. You do not multiply 500 times 15 because the cells are smaller than the scale representation so you divide.
Proposed Exercise: Conservation of the Linear Moment
Consider a block of M grease originally kept at rest on an inclined plane, without friction, by a block A. If a mass bullet m is fired with a velocity v against the block, getting stuck in it, find an expression for the distance d that the "block+bullet" system will move up to the position where it stops momentarily. Tip: here it is necessary to decompose the speed for the calculations
Explanation:
Momentum is conserved when there is no net external force. So momentum is conserved in the direction parallel to the incline.
p₀ = p
m v cos θ = (m + M) vₓ
vₓ = m v cos θ / (m + M)
After the collision, energy is conserved.
PE = KE
(m+M) gh = ½ (m+M) vₓ²
gh = ½ vₓ²
h = vₓ² / (2g)
d sin θ = [m v cos θ / (m + M)]² / (2g)
d = [m v cos θ / (m + M)]² / (2g sin θ)
A Spring is pulled to 10cm and held in place with a force of 500N .what is the spring constant
We are given:
extension of the spring (x) = 10 cm OR 0.1 m
Force applied to keep it in position (F) = 500 N
Solving for the spring constant:
We know that F = kx (when the spring is extended)
replacing the variables with the given values
500 = k * 0.1
k = 5000 N/m
This means that to extend the spring by 1 m, we have to apply a force of 5000 N
Suppose an empty grocery cart rolls downhill in a parking lot. The cart has a maximum speed of 1.3 m/s when it hits the side of the store and comes to rest 0.30 s later. If an unbalanced force of —65 N stops the cart, what is the mass of the grocery cart?
The cart comes to rest from 1.3 m/s in a matter of 0.30 s, so it undergoes an acceleration a of
a = (0 - 1.3 m/s) / (0.30 s)
a ≈ -4.33 m/s²
This acceleration is applied by a force of -65 N, i.e. a force of 65 N that opposes the cart's motion downhill. So the cart has a mass m such that
-65 N = m (-4.33 m/s²)
m = 15 kg
Leoni is participating in four drawing competitions. If the probability of her losing any
drawing competition is 0.7, find the probability of her winning
a) at least one competition.
b) exactly two competitions.
Answer:
(a) [tex]Probability = 0.7599[/tex]
(b) [tex]Probability = 0.2646[/tex]
Explanation:
Represent losing with L and winning with W.
So:
[tex]L = 0.7[/tex] --- Given
[tex]n = 4[/tex]
Probability of winning would be:
[tex]W = 1 - L[/tex]
[tex]W = 1 - 0.7[/tex]
[tex]W = 0.3[/tex]
The question illustrates binomial probability and will be solved using the following binomial expansion;
[tex](L + W)^4 = L^4 + 4L^3W + 6L^2W^2 + 4LW^3 + W^4[/tex]
So:
Solving (a): Winning at least 1
We look at the above and we list out the terms where the powers of W is at least 1; i.e., 1,2,3 and 4
So, we have:
[tex]Probability = 4L^3W + 6L^2W^2 + 4LW^3 + W^4[/tex]
Substitute value for W and L
[tex]Probability = 4 * 0.7^3*0.3 + 6*0.7^2*0.3^2 + 4*0.7*0.3^3 + 0.3^4[/tex]
[tex]Probability = 0.7599[/tex]
Hence, the probability of her winning at least one is 0.7599
Solving (a): Wining exactly 2
We look at the above and we list out the terms where the powers of W is exactly 2
So, we have:
[tex]Probability = 6L^2W^2[/tex]
Substitute value for W and L
[tex]Probability = 6*0.7^2*0.3^2[/tex]
[tex]Probability = 0.2646[/tex]
Hence, the probability of her winning exactly two is 0.2646
At its peak, a tornado is 74.0 m in diameter and carries 335-km/h winds. What is its angular velocity in revolutions per second?
Answer:
0.399 rev/s
Explanation:
Given that,
The diameter of a tornado, d = 74 m
Radius, r = 37 m
Linear velocity, v = 335 km/h = 93.05 m/s
We need to find the angular velocity in revolutions per second. Let it is [tex]\omega[/tex]. The relation between angular velocity and linear velocity is as follows :
[tex]v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{93.0556}{37}\\\\\omega=2.51\ rad/s[/tex]
or
[tex]\omega=\dfrac{2.51}{2\pi}\\\\\omega=0.399\ rev/s[/tex]
So, the angular velocity of the blade is 0.399 rev/s.
The diagram shows the four primary steps in the production of work in a four-stroke heat engine.
What is the correct order in which these steps occur?
A. Y, W, X, z
B. X, Z, W. Y
C. W, X, Y, Z
D. Z, X, Y, W
Answer:
D- Z, X, Y, W
Explanation:
Correct on edge
three properties of an ideal fluid that obey Bernoulli’s principle
Answer:
Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquidor gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.
Three properties of an ideal fluid that obey Bernoulli’s principle are :
1) incompressible
2) subjected to conservative forces
3) non - viscous
What is Bernoulli's principle ?Bernoulli's principle states that as the speed of moving fluid increases , the pressure within fluid decreases or it states that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity.
As we know that Bernoulli's principle is only valid for ideal fluids which have following properties :
1) Should be incompressible
2) subjected to conservative forces
3) It should be non - viscous which means there is no internal friction in the flow .
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Answer:
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Explanation:
The torque applied will be the average of the 3 torque calculated.
Torque = 12.01 Nm
Torque of a couple is the product of a force and its perpendicular distance to the direction of the force. Torque is synonymous to moment.
From the question, the given radius is 0.53m. The perpendicular distance for each torque will be 2 x 0.53 = 1.06 m
We will calculate for each torque
T1 = F1d
T1 = 8 x 1.06 = 8.48 Nm
T2 = F2d
T2 = 15 x 1.06 = 15.9 Nm
T3 = F3d
T3 = 11 x 1.06 = 11.66 Nm
The torque applied will be the average of the 3 torque calculated. That is,
Torque = (8.48 + 15.9 + 11.66)/3
Torque = 36.04 /3
Torque = 12.01 Nm
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When were Earth’s landmasses first recognizable as the continents we know today? 10 million years ago 135 million years ago 180 million years ago 300 million years ago
Answer:
b
Explanation:
i took the test
Earth’s landmasses were first recognized as the continents we know today
135 million years ago.
Landmass is defines as a large area of land. It can also be referred to as the
continents we have today. There are seven types of earth landmasses and
they are
Asia, Africa, North America, South America, Antarctica, Europe, and Australia.They were first discovered around 135 million years ago by the early
dwellers of the earth.
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An 800 kg car is parked next to a 1000 kg car. Their centers of mass are 3.5 m apart. Find the gravitational force between them.
Answer:
4.356e-6 Newtons
Explanation:
Using the equation for the force of gravity F=[tex]\frac{Gm_1m_2}{r^2}[/tex]. The two masses are m1=800kg and m2=1000 kg. The value of G, the gravitational constant =6.67e-11. The problem states the distance between the center of masses of the two cars is 3.5 meters(r). Plugging in what we have from the problem, you will get 4.346e-6 newtons. This makes sense as gravity in itself is a weak force requiring extremely massive objects to result in a noticeable force.
If you can run 10.43 m in 14.22 s. How fast are you running?
Answer:
I am 15th in my state for 55m hurdles with a time of 10.4 seconds
Explanation:
BAM
Answer: 44 m per minute
Explanation:
he triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 2.80 cm, producing an angular acceleration of the forearm of 145 rad/s2. What is the moment of inertia of the boxer's forearm
Answer:
Moment of inertia = 0.3862kg-m²
Explanation:
2.00x10³
2.80cm
145 rad
r = r⊥ x F
F is an applied force
r⊥ is the distance between the applied force and axis
Force exerted = 2.00x10³
r⊥ = 2.8cm = 0.028m
Alpha = 145rad/s²
r = 0.028m x 2.00x10³
r = 56.0N-m
To get the moment of inertia
56.0N-m² = (145rad/s²) x I
The I would be:
I = (56.0N-m²)/(145rad/s²)
I = 56/145
= 0.3862Kg-m²
This is the moment of inertia.
Thank you!
what causes diffferent air density?
Answer:
The temperature and gravity both affects the density
A 1400 kg car traveling in the positive direction takes 11.0 seconds to slow from 25.0 meters per second to 12.0 meters per second. What is the average force on the car during this time?
Answer:
–1652 N. The negative sign indicate that the force is in opposite direction to car.
Explanation:
The following data were obtained from the question:
Mass (m) of car = 1400 kg
Time (t) = 11 s
Initial velocity (u) = 25 m/s
Final velocity (v) = 12 m/s
Force (F) applied on the car =?
Next, we shall determine the acceleration of the car. This can be obtained as follow:
Time (t) = 11 s
Initial velocity (u) = 25 m/s
Final velocity (v) = 12 m/s
Acceleration (a) =?
a = (v – u) /t
a = (12 – 25) /11
a = –13/11
a = –1.18 m/s²
Finally, we shall determine the force on the car as follow:
Acceleration (a) = –1.18 m/s²
Mass (m) of car = 1400 kg
Force (F) applied on the car =?
F = ma
F = 1400 × –1.18
F = –1652 N
Thus, the force on the car is –1652 N. The negative sign indicate that the force is in opposite direction to car.
Fossils remains of Cynognathus , a triassic land reptile, have been found at both South America And Africa . What does this imply?
A. these continents used to be connected and later moved apart
B . People can find really cool fossils in random locations
C . the Cynognathus reptile evolved independently on 2 separate continents
D . the Cynognathus is found on both continents because it swam across the ocean
The discovery of fossils remains of Cynognathus at both South America And Africa suggests that these continents used to be connected and later moved apart.
What is the continental drift theory?According to continental drift theory:
"All of the continents were once together as a single continent named Pangaea, which was surrounded by a Mega Ocean known as Panthalassa."
Who proposed this theory?The continental drift theory was first proposed by Abraham Ortelius in 1596, and Alfred Wegener developed it in 1912.
If continental drift had not occurred what would be the explanation?On distinct continents, the species evolved independently. orTo form a second population, they swam to the opposite continent in breeding pairs.To learn more about fossils, continents, continental drift, and Pangaea here,
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If you jump upward with a speed of 1.70 m/s how high will you be when you stop rising?
Answer:
How long do you jump (sec) ?
Explanation:
How much work is required to stretch a spring 0.133 m if its force constant is 9.67 N/m?
Answer:
refer to attachment
Explanation:
hope it will helps u
Answer: 5cm
Explanation:
What happens to the mechanical advantage of a machine if the output force is less than the input force? What must happen to output distance? Give an example of a machine that does this?
The most commonly accepted theory of muscle growth states that ______________ ________ within a muscle activate a(n) ________________ response process that causes dormant cells to build and regenerate muscle tissue.
A. contractions; inhibitory
B. tension; neurological
C. microscopic tears; inflammatory
D. stress; cytokines
Answer:
C
Explanation:
The most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.
What is the significance of the microscopic tears in muscle?It has negative consequences on the muscle, and it is also known as "microtrauma," which occurs as a result of muscle contraction and is a normal part of the muscle repair and growth process. Here, the fibers in the muscle are damaged, and in response, the body initiates a repair process. This leads to muscle growth and increased strength and is helpful for muscle repair.
Hence, the most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.
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Three persons wants to push a wheel cart in the direction marked x in Fig. [04 Marks] The two person push with horizontal forces F1 and F2 as F1 = 45 N 70degree And F2 = 75 N , 20 Degree (a) Find the magnitude and direction of the force that third person should exert to stop this cart. You can ignore the effects of friction. (b) If the third person exerts the force found in part (a), the cart accelerates at 200 m/S2 in the (+) x-direction. What is the weight of the cart?
Answer:
a) F₃ = 108.71 N , θ = 218.68º b) m = 0.8487 kg
Explanation:
a) To solve this problem we will use Newton's second law, in the first part the accuracy is zero
∑ F = 0
X axis
F₁ₓ + F₂ₓ + F₃ₓ = 0
F₃ₓ = - F₁ₓ -F₂ₓ
Y axis
[tex]F_{1y}[/tex] + F_{2y} + F_{3y} = 0
F3y = -F_{1y} -F_{2y}
Let's use trigonometry to find the components of the applied forces
cos 70 = F₁ₓ / F₁ F₁ₓ = F₁ cos 70
sin 70 = F_{1y} / F₁ F_{1y} = F₁ sin 70
cos 20 = F₂ₓ / F2 F₂ₓ = F₂ cos 70
sin 20 = F_{2y} / F₂ F_{2y} = F₂ sin 70
F₁ₓ = 45 cos 70 = 15.39 N
F_{1y} = 45 sin 70 = 42.29 N
F₂ₓ = 75 cos 20 = 70.48 N
F_{2y} = 75 sin 20 = 25.65 N
let's calculate
F₃ₓ = -15.39 - 70.48
F₃ₓ = -85.87 N
F_{3y} = -42.29 - 25.65
F_{3y} = -67.94 N
this is the force that must be applied to keep the system in equilibrium, we can give this value in the form of module and angle
F₃ = √ (F₃ₓ² + F_{3y}²)
F₃ = √ (85.87² +67.94²)
F₃ = 108.71 N
tan θ = F₃ = [tex]F_{3y}[/tex] / F₃ₓ
θ = tan⁻¹ (67.94 / 84.87)
θ = 38.68º
Since the two values are negative, this angle is in the third quadrant, therefore the measuring angle n counterclockwise from the positive side of the x-axis is
θ = 180 + 38.68
θ = 218.68º
b) It is not clear, but we must suppose that the person exerts this force F3 in the direction of movement, bone at an angle θ= 39.68º, in this case Newton's equation for the x axis remains
F₁ₓ + F₂ₓ + F₃ₓ = m a
m = (F₁ₓ + F₂ₓ + F₃ₓ) / a
let's calculate
m = (15.39 + 7048 + 85.87) / 200
m = 0.8487 kg
what is the relevant similarity of the following argument?
"Tolerating a vicious dictator is like tolerating a bully on the block. If you let the bully push you around, sooner or later he will beat you up and take everything you have. If you let a dictator have his way, he will abuse his people and rob them of life and liberty. If you stand up to the bully just once or- better yet- knock him senseless with a stick, he will never bother you again. LIkewise, if you refuse to be coerced by a dictator or if you attack him, his reign will be over. Therefore, the best course of action for people oppressed by a dictator is to resist and attack."
a.
there are no relevant similarities
b.
tolerating a bully or dictator leads to further abuse
c.
the best course of action for people oppressed by a dictator is to resist and attack.
1. Two forces F~
1 and F~
2 are acting on a block of mass m=1.5 kg. The magnitude of
force F~
1 is 12N and it makes an angle of θ = 37◦ with the horizontal as shown in
figure-1. The block is sliding at a constant velocity over a frictionless floor.
Figure-1
(a) Find the value of the normal force on the block.
[3 marks]
(b) Find the magnitude of force F~
2 that is acting on the block
[4 marks]
(c) Find the magnitude of force F~
2 if the block accelerates with a magnitude of
a = 2.5 m/s2 along the direction of F~
2 . [3 mark
Answer:
(a) Normal force=7.48 N
Explanation:
N+F~1 sinθ-mg=0
=>N=1.5*9.8-12 sin37◦
=>N=14.7-7.22=7.48 N
what is mechanical energy?
a. the energy associated with the motion, position, or deformation of objects
b. the energy due only to the motion of an object or its component particles
c. the energy due only to the height of an object above a surface
D. the energy contained within the atomic nuclei of atoms
Answer:
A for sure
Explanation:
Why light travels slower in glass than in air or vacuum?
Answer:
because of glass' higher refractive index
Explanation:
air and vacuum have a lower refractive index and are optically lighter, so light travels faster.
whereas glass has a higher optical density, so light travels slower
1. Newton's 3rd Law states...
a. Objects in motion stay in motion and objects at rest stay at rest
b. Force is equal to mass times acceleration
c. For each action there is an equal and opposite reaction
Answer:
C
Explanation:
There's a reason newton's 3rd law is called action-reaction :D
A - 1st law/inertia
B - 2nd law/f=ma
Newton's third law of motion states that for each action there is an equal and opposite reaction or force. Thus, the correct option is C.
What is Newton's third law of motion?Newton's third law of motion states that for every action or force applied in nature there is an equal and opposite reaction or force.
According to Newton's third law of Motion, if an object A exerts a force on the object B, then the object B must exert a force which is of equal magnitude and opposite direction back on the object A. This law represents symmetry in nature with the forces which are always occur in pairs, and one body cannot exert a force which is on another object without experiencing a force itself.
Therefore, the correct option is C.
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An oil refinery uses a Venturi tube to measure the flow rate of gasoline. The density of the gasoline is
ρ = 7.40 ✕ 102 kg/m3,
the inlet and outlet tubes, respectively, have a radius of 3.74 cm and 1.87 cm, and the difference in input and output pressure is
P1 − P2 = 1.20 kPa.
a) find the speed of the gasoline as it leaves the hose
b) find the fluid flow rate in cubic meters per second
Answer:
(a) V₂ = 1.86 m/s
(b) Q = 5.1 x 10⁻⁴ m³/s
Explanation:
(a)
The formula derived for Venturi tube is as follows:
P₁ - P₂ = (ρ/2)(V₂² - V₁²)
where,
P₁ - P₂ = Difference in Pressure of Inlet and Outlet = 1.2 KPa = 1200 Pa
ρ = Density of Gasoline = 7.4 x 10² kg/m³
V₂ = Exit Velocity = ?
V₁ = Inlet Velocity
Therefore,
1200 Pa = [(7.4 x 10²kg/m³)/2](V₂² - V₁²)
V₂² - V₁² = (1200 Pa)/(3.7 x 10² kg/m³)
V₂² - V₁² = 3.24 m²/s² ------------------- equation (1)
Now, we will use continuity equation:
A₁V₁ = A₂V₂
where,
A₁ = Inlet Area = πd₁²/4 = π(0.0374 m)²/4 = 1.098 x 10⁻³ m²
A₂ = Exit Area = πd₂²/4 = π(0.0187 m)²/4 = 2.746 x 10⁻⁴ m²
Therefore,
(1.098 x 10⁻³ m²)V₁ = (2.746 x 10⁻⁴ m²)V₂
V₁ = (2.746 x 10⁻⁴ m²)V₂/(1.098 x 10⁻³ m²)
V₁ = 0.25 V₂
using this value in equation (1):
V₂² - (0.25 V₂)² = 3.24 m²/s²
0.9375 V₂² = 3.24 m²/s²
V₂² = (3.24 m²/s²)/0.9375
V₂ = √(3.456 m²/s²)
V₂ = 1.86 m/s
(b)
For fluid flow rate we use the following equation:
Flow Rate = Q = A₂V₂ = (2.746 x 10⁻⁴ m²)(1.86 m/s)
Q = 5.1 x 10⁻⁴ m³/s
The formula for finding variables in a Venturi tube is shown below:
The speed of the gasolineP₁ - P₂ = (ρ/2)(V₂² - V₁²)
where, P₁ - P₂ is difference in pressure of Inlet and outlet, ρ = density, V₂ = exit velocity and V₁ is inlet velocity
P₁ - P₂ = 1.2 KPa = 1200 Pa
ρ = 7.4 x 10² kg/m³
V₂ = Exit Velocity = ?
V₁ = Inlet Velocity
We then substitute the variables into this equation.
P₁ - P₂ = (ρ/2)(V₂² - V₁²)
1200 Pa = [(7.4 x 10²kg/m³)/2](V₂² - V₁²)
V₂² - V₁² = (1200 Pa)/(3.7 x 10² kg/m³)
V₂² - V₁² = 3.24 m²/s² ------ equation (1)
The continuity equation A₁V₁ = A₂V₂ is then used
where,A₁ = Inlet area = πd₁²/4 = π(0.0374 m)²/4 = 1.098 x 10⁻³ m²
A₂ = Exit Area = πd₂²/4 = π(0.0187 m)²/4 = 2.746 x 10⁻⁴ m²
(1.098 x 10⁻³ m²)V₁ = (2.746 x 10⁻⁴ m²)V₂
V₁ = (2.746 x 10⁻⁴ m²)V₂/(1.098 x 10⁻³ m²)
V₁ = 0.25 V₂
We then substitute the value into equation 1
V₂² - (0.25 V₂)² = 3.24 m²/s²
0.9375 V₂² = 3.24 m²/s²
V₂² = (3.24 m²/s²)/0.9375
V₂ = √(3.456 m²/s²)
V₂ = 1.86 m/s
The fluid flow rate we use the following equation:This can be calculated using the formula
Flow Rate = Q = A₂V₂
= (2.746 x 10⁻⁴ m²)(1.86 m/s)
= 5.1 x 10⁻⁴ m³/s
A car Excel accelerates from rest to a velocity of 5 m/s in 4 seconds. What is its average acceleration over this period of time
Answer:
1.25
Explanation:
acceleration = velocity÷time
Answer:
Its acceleration is 1.25 meters/second2
Explanation:
The car's average acceleration would be 1.25m/s^2 or 1.25meters/second/second. That looks to be the fourth one you've listed.
A golf ball (m=26.7g) is struck a blow that makes an angle of 33.6 degrees with the horizontal. The drive lands 190m away on a flat fairway. The acceleration of gravity is 9.8 m/s^2 . If the golf club and ball are in contact for 7.13 ms, what is the average force of impact?
Answer:
Th average force impact is [tex]F = 168.298 \ N[/tex]
Explanation:
From the question we are told that
The mass of the golf ball is [tex]m_g = 26.7 \ g = 0.0267 \ kg[/tex]
The angle made is [tex]\theta = 33.6 ^o[/tex]
The range of the golf ball is [tex]R = 190 \ m[/tex]
The duration of contact is [tex]\Delta t = 7.13 \ ms = 7.13 *10^{-3} \ s[/tex]
Generally the range of the golf ball is mathematically represented as
[tex]R = \frac{v^2 sin2(\theta)}{g}[/tex]
Here v is the velocity with which the golf club propelled it with, making v the subject
[tex]v = \sqrt{\frac{R * g}{sin 2 (\theta)} }[/tex]
=> [tex]v = \sqrt{\frac{190 * 9.8}{sin 2 (33.6)} }[/tex]
=> [tex]v = 44.94 \ m/s[/tex]
Generally the change in momentum of the golf ball is mathematically represented as
[tex]\Delta p = m * (v - u )[/tex]
here u is the initial velocity of the ball before being stroked and the value is 0 m/s
[tex]\Delta p = 0.0267 * ( 44.94 - 0 )[/tex]
=> [tex]\Delta p = 1.19996 \ kg \cdot m/s[/tex]
Generally the average force of impact is mathematically represented as
[tex]F = \frac{\Delta p }{\Delta t}[/tex]
=> [tex]F = \frac{1.19996 }{7.13 *10^{-3}}[/tex]
=> [tex]F = 168.298 \ N[/tex]
