1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ket [755]
3 years ago
12

A 0.25 kg ball is suspended from a light 0.65 m string as shown. The string makes an angle of 31° with the vertical. Let U = 0 w

hen the ball is at its lowest point (θ = 0).
a) What is the gravitational potential energy, in joules, of the ball before it is released?
b) What will be the speed of the ball, in meters per second, when it reaches the bottom?
Physics
2 answers:
steposvetlana [31]3 years ago
8 0

Answer:

a. 0.23J

b. 1.35 m/s

Explanation:

a. U = mgh where where m = mass of the object, g = acceleration due to gravity, and h = height

h = L - Lcos(θ) where L = length of the rope, and θ = angle with respect to vertical.

Therefore, U = mg(L - Lcos(θ))

U = 0.25 * 9.8 (0.65m - 0.65cos(31° ))

U = 0.2275 ≈ 0.23J

The gravitational potential energy of the ball before it is released = 0.23J

b. To determine the velocity of the object at the bottom of its motion, all of the energy has gone from gravitational potential into kinetic since at the bottom, the problem says that U = 0. The kinetic energy of an object is given by the following equation:  

K.E=\frac{I}{2}*mv^{2}

where m = mass of the object and v = velocity of the object. Since we know that all of the energy was transferred into kinetic energy at the bottom, we can conclude that:

0.2275=\frac{1}{2} *0.25*v^{2}

v^{2}=\frac{2*0.2275}{0.25}

v^{2}=1.82

v=\sqrt{1.82}=1.3491\\ ≈ 1.35m/s

Therefore, the speed of the ball when it reaches the bottom = 1.35m/s

 

steposvetlana [31]3 years ago
5 0

Explanation:

a) The height of the ball h with respect to the reference line is

h = L - L\cos{31°} = L(1 - \cos{31°})

so its initial gravitational potential energy U_0 is

U = mgh = mgL(1 - \cos{31°})

\:\:\:\:\:=(0.25\:\text{kg})(9.8\:\text{m/s}^2)(0.65\:\text{m})(1 - \cos{31})

\:\:\:\:\:=0.23\:\text{J}

b) To find the speed of the ball at the reference point, let's use the conservation law of energy:

\Delta{K} + \Delta{U} = 0 \Rightarrow K_0 + U_0 = K + U

We know that the initial kinetic energy K_0, as well as its final gravitational potential energy U are zero so we can write the conservation law as

mgL(1 - \cos{31°}) = \frac{1}{2}mv^2

Note that the mass gets cancelled out and then we solve for the velocity v as

v = \sqrt{2gL(1 - \cos{31°})}

\:\:\:\:\:= \sqrt{2(9.8\:\text{m/s}^2)(0.65\:\text{m})(1 - \cos{31°})}

\:\:\:\:\:= 1.3\:\text{m/s}

You might be interested in
Determine the maximum shearing stress in a solid shaft of 1.5-in. diameter as it transmits 75 hp at a speed of 1800 rpm. (Round
erma4kov [3.2K]

Answer:

\tau=3.96\ ksi

Explanation:

Given that

d= 1.5 in                      ( 1 in = 0.0254 m)

d= 0.0381 m

P= 75 hp                      ( 1 hp = 745.7 W)

P= 55927.5 W

N= 1800 rpm

We know that power P is given as

P=\dfrac{2\pi N\ T}{60}

T=Torque

N=Speed

55927.5=\dfrac{2\times \pi \times 1800\ T}{60}

T=296.85 N.m

The maximum shear stress is given as

\tau=\dfrac{16 T}{\pi d^3}

\tau=\dfrac{16\times 296.85}{\pi \times 0.0381^3}

\tau=27.35\ MPa

We know that 1 MPa =0.145 ksi

\tau=3.96\ ksi

3 0
3 years ago
Which of the following is true regarding the Earth's mantle?
Brilliant_brown [7]
B) It’s material moves due to convection currents.
6 0
3 years ago
5 What is the kinetic energy of a 28 kg car moving at a velocity of 7 m/s O 1963 98 686 J O 350 nocter diagram, at which point w
Shtirlitz [24]

Answer:

98 joules

Explanation:

1/2 of 28 = 14

14 multiply by 7= 98 joules

4 0
3 years ago
Technician A says that the freezing point of a substance is the temperature at which the substance changes state from a solid to
pashok25 [27]

Answer:

Technician B is correct

Explanation:

Freezing is a method of conversion of substance in its liquid state to solid state. It is the process by which a liquid substance changes to a solid at a particular temperature.

Increasing the pressure and decreasing the temperature of a liquid increases its freezing point. For example, in other to freeze water i.e to change water to ice, it has to be kept in a fridge at a temperature lower than the temperature of the water. The essence of covering the fridge after placing the water in the fridge is to increase the pressure of the liquid hence increasing its freezing rate.

Based on the above explanation, it can be concluded that technician B is correct.

5 0
3 years ago
Which best describes how geothermal energy is used to make electricity?. . A.. Rocks are split to release energy that drives a s
In-s [12.5K]
Answer is b that is  Heat energy from below the ground converts water to steam to drive a steam turbine attached to an electrical generator.. . 
6 0
3 years ago
Other questions:
  • A rubber balloon has become negatively charged from being rubbed with a wool cloth, and the charge is measured as 1.00 × 10−14 C
    13·1 answer
  • An electric field of 710,000 N/C points due west at a certain spot. What is the magnitude of the force that acts on a charge of
    5·1 answer
  • A light bulb radiates 110 nW of single-frequency sinusoidal electromagnetic waves uniformly in all directions. Calculate the ave
    5·1 answer
  • ________ occurs when an object in the outer reaches of the solar system passes between earth and a far distant star, temporarily
    6·1 answer
  • A bike is moving at a velocity of 50 m/s. It increases in velocity until it reaches 150 m/s in seconds. What is the acceleration
    15·1 answer
  • The fast server in women's tennis is Venus Williams, who recorded a serve of 130   (209  ) in 2007.
    15·1 answer
  • Se lanza verticalmente hacia arriba una piedra con una velocidad de 125km/h.
    8·1 answer
  • How did black holes get their name
    13·1 answer
  • A rubber ball and a steel ball are dropped from the same height onto a concrete floor. They have the same mass, and lets assume
    8·1 answer
  • The idea that the Earth sits motionless in the Universe at the center of a revolving globe of stars, with the Moon and planets i
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!