While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge. The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m. At what time intervals does Sheila encounter her brother, if she rides opposite to the direction of rotation of the merry-go-round?
a. 5.03 s
b. 8.37 s
c. 12.6 s
d. 25.1 s
e. 50.2 s

Answer:

a. 42N

b. 11.8m/s

c. 1.69s

d. 160N

Explanation:

a)  The tension of the rope is 130.66 N.

b) The speed of the bucket while strike the water = 4.64 m/s.

c) The time of fall is  = 4.303 second.

d)  While the bucket is falling, what is the force exerted on the cylinder by the axle is  130.66 N.

Mass of the water bucket; M = 15.0 kg

Mass of the cylinder; m =  12.0 kg

Height of the bucket; h = 10.0 m.

They are connected by a rope and a pivots.

So, acceleration of them is same and let it be a.

So equation of motion of both of them be:

Mg - T = Ma

and, T - mg = ma

Hence, a = g(M-m)/(M+m)

= 9.8(15-12)/(15+12)

= 1.08 m/s²

And, T = m(g+a)

= 12.0(9.8+1.08)

= 130.66 N.

a) so tension of the rope is 130.66 N.

b) speed of the bucket while strike the water = √2ah =√(2×1.08×10.0) m/s = 4.64 m/s.

c) The time of fall is = √2h/a = √(2×10/1.08) second = 4.303 second.

d) While the bucket is falling, what is the force exerted on the cylinder by the axle is tension of the rope, that is, 130.66 N.

Learn more about speed here:

https://brainly.com/question/28224010

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Answer:

  c.  in the absence of an unbalanced force, an object at rest will stay at rest and an object in motion will stay in motion.

Explanation:

First law: things keep doing what they are doing, unless force is applied.

Complete question is;

Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charge the battery with power rating, 12 V, 50 Ampere-minutes

Answer:

Amount of water required to charge the battery = 7.35 m³

Explanation:

The formula for Potential energy of the water at that height = mgh

Where;

m = mass of the water

g = acceleration due to gravity = 9.8 m/s²

H = height of water = 50 cm = 0.5 m

We know that in density, m = ρV

Where;

ρ = density of water = 1000 kg/m³

V = volume of water

So, potential energy is now given as;

Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J

Now, formula for energy of the battery is given as;

E = qV

We are given;

q = 50 A.min = 50 × 60 = 3,000 C

V = 12 V

Thus;

qV = 3,000 × 12 = 36,000 J

E = 36,000 J

At a 100% conversion rate, the energy of the water totally powers the battery.

Thus;

(4900V) = (36,000)

4900V = 36,000

V = 36,000/4900

V = 7.35 m³

Answer:

Explanation:

The power rating of the battery isn't provided. But let us assume that it is one of the common batteries with ratings of 12 V and 50 A.h

Potential energy possessed by water at that height = mgh

m = mass of the water = ρV

ρ = density of water = 1000 kg/m³

V = volume of water = ?

g = acceleration due to gravity = 9.8 m/s²

h = height of water = 50 cm = 0.5 m

Potential energy = ρVgh = 1000 × V × 9.8 × 0.5 = (4900V) J

Energy of the battery = qV

q = 50 A.h = 50 × 3600 = 180,000 C

V = 12 V

qV = 180,000 × 12 = 2,160,000 J

Energy = 2,160,000 J

At a 100% conversion rate, the energy of the water totally powers the battery

(4900V) = (2,160,000)

4900V = 2,160,000

V = (2,160,000/4900)

V = 440.82 m³

Hence, with our assumed power ratings for the battery (12 V and 50 A.h), 440.82 m³ of water at the given height of 50 cm would power the battery.

Incase the power ratings of the battery in the complete question is different, this solution provides you with how to obtain the correct answer, given any battery power rating.

Hope this Helps!!!

Answer:

The final speed of the ball is 9 m/s.

Explanation:

We have,

A steel ball is dropped from a diving platform. It is required to find the velocity of the ball 0.9 seconds after its released. It will move under the action of gravity. Using equation of motion to find it as :

[tex]v=u+at[/tex]

u = 0 (at rest), a = g

[tex]v=gt\\\\v=10\times 0.9\\\\v=9\ m/s[/tex]

So, the final speed of the ball is 9 m/s.

Answer: [tex]2m/s^2[/tex]

Explanation:

[tex]Formula: F=ma[/tex]

Where;

F = force

m = mass

a = acceleration

Solve for a;

[tex]a=\frac{F}{m}[/tex]

[tex]a=\frac{30N}{15kg}\\ a=2m/s^2[/tex]

Answer:

The power is  [tex]P_p = 4.6 \ W[/tex]

Explanation:

From the question we are told that

   The power delivered is  [tex]P_{s} = 1.15 \ W[/tex]

   Let it resistance be denoted as R

    The resistors are connected in series so the equivalent resistance is  

     [tex]R_{eqv} = R+ R = 2 R[/tex]

Considering when it is connected in series    

Generally power is mathematically represented as

     [tex]P_s = V * I[/tex]

Here I is the current which is mathematically represented as

       [tex]I = \frac{V}{2R}[/tex]

The power becomes

     [tex]P_s = V * \frac{V}{2R}[/tex]

     [tex]P_s = \frac{V^2}{2R}[/tex]

substituting value

    [tex]1.15 = \frac{V^2}{2R}[/tex]

Considering when resistance is connected in parallel

  The equivalent resistance becomes

    [tex]R_{eqv} = \frac{R}{2}[/tex]

So The current  becomes

       [tex]I = \frac{V}{\frac{R}{2} } = \frac{2V}{R}[/tex]

And the power becomes

     [tex]P_p = V * \frac{2V}{R} = \frac{2V^2}{R} = \frac{4 V^2}{2 R} = 4 * P_s[/tex]

 substituting values

     [tex]P_p = 4 * 1.15[/tex]

     [tex]P_p = 4.6 \ W[/tex]

Answer:

Cube temperature = 526.83 K

Explanation:

Volume of the cube and sphere will be the same.

Now, volume of cube = a³

And ,volume of sphere = (4/3)πr³

Thus;

a³ = (4/3)πr³

a³ = 4.1187r³

Taking cube root of both sides gives;

a = 1.6119r

Formula for surface area of sphere is;

As = 4πr²

Also,formula for surface area of cube is; Ac = 6a²

Thus, since a = 1.6119r,

Then, Ac = 6(1.6119r)²

Ac = 15.5893r²

The formula for radiant power is;

Q' = eσT⁴A

Where;

e is emissivity

σ is Stefan boltzman constant = 5.67 x 10^(-8) W/m²k

T is temperate in kelvin

A is Area

So, for the cube;

(Qc)' = eσ(Tc)⁴(Ac)

For the sphere;

(Qs)' = eσ(Ts)⁴(As)

We are told (Qc)' = (Qs)'

Thus;

eσ(Tc)⁴(Ac) = eσ(Ts)⁴(As)

eσ will cancel out to give;

(Tc)⁴(Ac) = (Ts)⁴(As)

Since we want to find the cube's temperature Tc,

(Tc)⁴ = [(Ts)⁴(As)]/Ac

Plugging in relevant figures, we have;

(Tc)⁴ = [556⁴ × 4πr²]/15.5893r²

r² will cancel out to give;

(Tc)⁴ = [556⁴ × 4π]/15.5893

Tc = ∜([556⁴ × 4π]/15.5893)

Tc = 526.83 K

Answer:

Spring Constant = 279.58 N/m

Explanation:

We are given;

Mass; m = 2.05 x 10^(-2) kg = 0.0205 kg

Distance of compression; x = 8.01 × 10^(-2) m = 0.0801 m

Maximum height; h = 4.46 m

The formula for the energy in the spring is given by;

E = ½kx²

where:

k is the spring constant

x is the distance the spring is compressed.

Now, this energy of the spring will be equal to the energy of the pellet at its highest point. Energy of pallet = mgh So;

½kx² = mgh

Plugging in the relevant values, we have;

½ * k * 0.0801² = 0.0205 * 9.81 * 4.46

0.003208005k = 0.8969

k = 0.8969/0.003208005

k = 279.58 N/m

Answer:

To solve this problem we just need to graph two forces with same direction, pointing to different sides with intensities of 40 N and 60 N.

The image attached shows these forces.

Notice that the vectors are parallel, that's because they have the same direction, but they point to different sides, and their magnitudes have a difference of 20 N.

Answer:

0.981 rad/sec^2

Explanation:

mass that pulls on string = 5 kg

weight due to mass = 5 x 9.81 = 49.05 N

radius of rod = 0.1 m

torque produced by this force on the rod = force x radius

torque = 49.05 x 0.1 = 4.905 N-m

mass of disk = 125 kg

radius of disk = 0.2 m

moment of inertia of the disk I = m[tex]r^{2}[/tex]

I = 125 x [tex]0.2^{2}[/tex] = 5 kg-m^2

from the equation, T = Iα

where T is torque

I is moment of inertia

α is angular acceleration

imputing values,

4.905 = 5α

α = 4.905/5 = 0.981 rad/sec^2

Answer:

29.16 J

Explanation:

From Hook's law,

W = 1/2(ke²)..................... Equation 1

Where W = work done, k = Spring constant, e = extension.

Given: W = 9 J, e = 0.5 m.

Substitute into equation 1

9 = 1/2(k×0.5²)

Solve for k

k = 18/0.5²

k = 72 N/m.

The work done required to stretch the spring by additional 0.4 m is

W = 1/2(72)(0.4+0.5)²

W = 36(0.9²)

W = 29.16 J.

Answer:

If the acceleration is constant, the movements equations are:

a(t) = A.

for the velocity we can integrate over time:

v(t) = A*t + v0

where v0 is a constant of integration (the initial velocity), for the distance traveled between t = 0 units and t = 10 units, we can solve the integral:

[tex]\int\limits^{10}_0 {A*t + v0} \, dt = ((A/2)10^2 + v0*10) = (A*50 + v0*10)[/tex]

Where to obtain the actual distance you can replace the constant acceleration A and the initial velocity v0.

Answer:

  a = - e E / m

a = - 1,758 10¹¹ E

Explanation:

For this exercise we can use Newton's second law

        F = m a

where the force is electric

 the forces given by the product of the charge by the electric field

         F = q E

in this case tell us that the charge is the charge of the electron

         q = -e = - 1.6 10⁻¹⁹ C

we substitute

        - e E = m a

          a = - e E / m

we calculate

           a = - 1.6 10⁻¹⁹ / 9.1 10⁻³¹ E

           a = - 1,758 10¹¹ E

The negative sign indicates that the acceleration is in the opposite direction to the electric field

Answer:

A burning candle. (chemical energy into energy of heat and light, i.e. thermal and wave)

Explanation:

Answer:

The width of the slit will be ".946 mm".

Explanation:

The given values are:

Wavelength = 610 × 10⁻⁹

Length, L = 3 m

As we know,

⇒  [tex]\frac{y}{L} = \frac{m(wavelength)}{a}[/tex]

On putting the estimated values, we get

⇒  [tex]\frac{2\times 10^{-3}}{3.1} = \frac{(1)(610 X 10^{-9})}{a}[/tex]

On applying cross-multiplication, we get

⇒  [tex]a=9.46\times 10^{-4}[/tex]

⇒  [tex]a = .946 mm[/tex]

Answer:

Explanation:

Using the law of conservation of momentum which states that 'the sum of momentum of bodies before collision is equal to their sum after collision. The bodies will move together with a common velocity after collision.

Momentum = Mass * Velocity

Before collision;

Momentum of receiver m1u1= 0 kgm/s (since the receiver is standing still)

Momentum of the tackler

m2u2 = 2.60*122 = 317.2 kgm/s

where m2 and u2 are the mass and velocity of the tacker respectively.

Sum of momentum before collision = 0+317.2 = 317.2 kgm/s

After collision

Momentum of the bodies = (m1+m2)v

v = their common velocity

m1 = mass of the receiver

Momentum of the bodies = (122+m1)(1.30)

Momentum of the bodies = 158.6+1.30m1

According to the law above;

317.2 = 158.6+1.30m1

317.2-158.6 = 1.30m1

158.6 = 1.30m1

m1 = 158.6/1.30

m1 = 122kg

The mas of the receiver is 122kg

Answer:

Explanation:

The Law of Energy Conservation states that K1 + U1 = K2 + U2

m= 72.0 kg

h= 3.90 m

a)

K1 + U1 = K2 + U2

0 + mgh = 1/2mvf^2 + 0

mass cancels out so gh=1/2vf^2

(9.8 m/s^2)(3.9 m)=(.5)(vf^2)

vf= 8.74 m/s

b)

1/2mv^2 + mgh = 1/2mv^2 + 0

mass cancels again

(.5)(2.9^2 m/s) + (9.8 m/s^2)(3.9 m) = (.5)(vf^2)

vf= 9.21 m/s

c)

This would be the same as the past problem as the velocity gets squared so direction along the axis doesn't matter. Thus, vf= 9.21 m/s

Answer:

Option B - displacement can be specified by a magnitude and a direction.

Explanation:

A Vector quantity is defined as a physical quantity characterized by the presence of both magnitude as well as direction. Examples include displacement, force, torque, momentum, acceleration, velocity e.t.c

Whereas a scalar quantity is defined as a physical quantity which is specified with the magnitude or size alone. Examples include length, speed, work, mass, density, etc.

Displacement is the difference between the initial position and the final position of a body. Displacement is a vector quantity and not a scalar quantity because it can be described by using both magnitude as well as direction.

Looking at the options, the only one that truly justifies this definition is option B.

Answer:

T₁ = 378.33 k = 105.33°C

Explanation:

From Fourier's Law of heat conduction, we know that:

Q = - KAΔT/t

where,

Q = Heat Transfer Rate = 1400 W

K = Thermal Conductivity of Material (Aluminum) = 237 W/m.k

A =Surface Area through which heat transfer is taking place=circular bottom

A = π(radius)² = π(0.15 m)² =  0.0707 m²

ΔT = Difference in Temperature of both sides of surface = T₂ - T₁

T₁ = Temperature of outer surface = ?

T₂ = Temperature of inner surface = 105°C + 273 = 378 k

ΔT = 388 k - T₁

t = thickness of the surface (Bottom of Pot) = 0.4 cm = 0.004 m

Therefore,

1400 W = - (237 W/m.k)(0.0707 m²)(378 k - T₁)/0.004 m

(1400 W)/(4188.14 W/k) = - (378 k - T₁)

T₁ = 0.33 k + 378 k

T₁ = 378.33 k = 105.33°C

Answer:

a = -0.8 m/s²

Here, negative sign indicates that the acceleration has opposite direction to the direction of motion.

Explanation:

First we find the angular acceleration of the ball from the following formula:

α = (ωf - ωi)/t

where,

α = angular acceleration = ?

ωf = final angular velocity = 7 rad/s

ωi = initial angular velocity = 13 rad/s

t = Time taken = 15 s

Therefore,

α = (7 rad/s - 13 rad/s)/15 s

α = - 0.4 rad/s

negative sign shows that acceleration is in opposite direction to the direction of motion.

Now, for the linear acceleration, we use the formula:

a = rα

where,

a = linear acceleration = ?

r = radius of circular path = length of rope = 2 m

therefore,

a = (2 m)(- 0.4 rad/s²)

a = -0.8 m/s²

Here, negative sign indicates that the acceleration has opposite direction to the direction of motion.

Answer:

W = 414 J, correct is B

Explanation:

Work is defined by

        W = ∫ F .dx

where F is the force, x is the displacement and the point represents the dot product

this expression can also be written with the explicit scalar product

        W = ∫ F dx cos θ

where is the angle between force and displacement

for this case as the force is constant

         W = F x cos θ

calculate

         W = 25.0 18.0 cos (-23)

         W = 414 J

the correct answer is B

Answer:

Answer D is correct

Explanation:

[tex]pressure = \frac{force}{area} \\ = \frac{320}{0.5} \\ = 640[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Complete Question

The complete question is shown on the first uploaded image

Answer:

The mass is    [tex]M =1.43 *10^{32} \ kg[/tex]

Explanation:

From the  question we are told that

       The mass of the stars are [tex]m_1 = m_2 =M[/tex]

        The orbital speed of each star is  [tex]v_s = 240 \ km/s =240000 \ m/s[/tex]

         The orbital period is [tex]T = 12.5 \ days = 12.5 * 2 4 * 60 *60 = 1080000\ s[/tex]

The centripetal force acting on these stars is mathematically represented as

      [tex]F_c = \frac{Mv^2}{r}[/tex]

The gravitational force acting on these stars is mathematically represented as

      [tex]F_g = \frac{GM^2 }{d^2}[/tex]

So  [tex]F_c = F_g[/tex]

=>        [tex]\frac{mv^2}{r} = \frac{Gm_1 * m_2 }{d^2}[/tex]

=>      [tex]\frac{v^2}{r} = \frac{GM}{(2r)^2}[/tex]

=>      [tex]\frac{v^2}{r} = \frac{GM}{4r^2}[/tex]

=>    [tex]M = \frac{v^2*4r}{G}[/tex]

The distance traveled by each sun in one cycle is mathematically represented as

     [tex]D = v * T[/tex]

      [tex]D = 240000 * 1080000[/tex]

      [tex]D = 2.592*10^{11} \ m[/tex]

Now this can also be represented as

      [tex]D = 2 \pi r[/tex]

Therefore

                  [tex]2 \pi r= 2.592*10^{11} \ m[/tex]

=>   [tex]r= \frac{2.592*10^{11}}{2 \pi }[/tex]

=>    [tex]r= 4.124 *10^{10} \ m[/tex]

So  

       [tex]M = \frac{v^2*4r}{G}[/tex]

=>    [tex]M = \frac{(240000)^2*4*(4.124*10^{10})}{6.67*10^{-11}}[/tex]

=>    [tex]M =1.43 *10^{32} \ kg[/tex]

Answer:

Explanation:

Volume of asteroid = 4/3 x π x 160³

= 17.15 x 10⁶

mass = volume x density

= 17.15 x 10⁶ x 2600

= 445.9 x 10⁸ kg

kinetic energy

= 1/2 x 445.9 x 10⁸  x( 12.6 )² x 10⁶

= 35.4 x 10¹⁷ J .

2 )

energy of 15 megaton

= 4.184 x 10¹⁵ x 15 J

= 62.76 x 10¹⁵ J

No of bombs required

= 35.4 x 10¹⁷ / 62.76 x 10¹⁵

= 56.4 Bombs .

Answer:

A and B is positive charge

C_negative

Explanation:

because when an ebonite is rubbed with fur produce negative charge due to law of electrostatic like charge repel and unlike attract

Answer with Explanation:

We are given that

Mass of spring,m=3 kg

Distance moved by object,d=0.6 m

Spring constant,k=210N/m

Height,h=1.5 m

a.Work done  to compress the spring initially=[tex]\frac{1}{2}kx^2=\frac{1}{2}(210)(0.6)^2=37.8J[/tex]

b.

By conservation law of energy

Initial energy of spring=Kinetic energy  of object

[tex]37.8=\frac{1}{2}(3)v^2[/tex]

[tex]v^2=\frac{37.8\times 2}{3}[/tex]

[tex]v=\sqrt{\frac{37.8\times 2}{3}}[/tex]

v=5.02 m/s

c.Work done by friction on the incline,[tex]w_{friction}=P.E-spring \;energy[/tex]

[tex]W_{friction}=3\times 9.8\times 1.5-37.8=6.3 J[/tex]

Answer:

x2 = 64 revolutions.

it rotate through 64 revolutions in the next 5.00 s

Explanation:

Given;

wheel rotates from rest with constant angular acceleration.

Initial angular speed v = 0

Time t = 2.50

Distance x = 8 rev

Applying equation of motion;

x = vt +0.5at^2 ........1

Since v = 0

x = 0.5at^2

making a the subject of formula;

a = x/0.5t^2 = 2x/t^2

a = angular acceleration

t = time taken

x = angular distance

Substituting the values;

a = 2(8)/2.5^2

a = 2.56 rev/s^2

velocity at t = 2.50

v1 = a×t = 2.56×2.50 = 6.4 rev/s

Through the next 5 second;

t2 = 5 seconds

a2 = 2.56 rev/s^2

v2 = 6.4 rev/s

From equation 1;

x = vt +0.5at^2

Substituting the values;

x2 = 6.4(5) + 0.5×2.56×5^2

x2 = 64 revolutions.

it rotate through 64 revolutions in the next 5.00 s

Answer:

32mi

Explanation:

If 1lb contains 3,500 Cal

It means the number of hours required to burn 3500cal would be;

3500/331 = 10.57hours

But a brisk walk is 3.0 mi/h,

It means a distance of 3.0 × 10.57 mi would be covered = 31.71 miles

32miles{ approximated to the nearest whole}

Note Distance = speed × time

Answer:  Its b, The only problem with this is is there supposed to be a picture?

Explanation: NASA has used there fancy gadgets to figure this out but if there was a picture, this answer could be different.