Chapter 10
What is the moment of inertial for a hollow sphere with mass 0.4kg and radius 100cm that also has a a solid disk with radius 300cm and mass 0.22kg on top of the sphere? Assume there is a axis of rotation throught the exact center of both object.
1.26 kg m2
A man is standing on a plank of wood suspended across a chasm. The man has a mass of 70kg and is wearing shoes each with a contact area of 0.015m2. The plank will break if more than 3000 Pa of force is applied. Will the man break the plank?
Yes
I apply a torque of 1000 Nm to a solid sphere. If the sphere has a angular acceleration of 10 rad/s2, and has a mass of 5kg, find the radius of the sphere.
7.07 m
A household AC power supply operates at a frequency of 50.0Hz. What is the period of this electrical signal?
0.020 s
A solid disk has a moment of inertia of 2.0 kg m2. The disk rotates at an angular velocity of 3.0 rad/s. what is the angular momentum?
A. 2.0 kg·m²/s
B. 3.0 kg·m²/s
C. 6.0 kg·m²/s
D. 12.0kg·m²/s
C
A solid sphere with mass 4kg and radius 0.6m has an angular acceleration of 7 rad/s2. If the axis of rotation is directly down the center, what force is being tangentially applied to the edge to achieve this angular acceleration?
6.72 N
What is the density of a ball that is 82.4% submerged in water? Rho water = 1000kg/m3.
824 kg/m3
A 2.0kg mass is attached to a massless string and moves in a circle of radius 600cm with a speed of 4.0m/s. What is the angular momentum of the mass about the center of the circle?
48 kg m2/s
A dolphin produces high-frequency sound pulses at 55kHz while navigating underwater. If the speed of sound in the water at 1500 m/s, determine the wavelength of these sound waves. What is the wavelength of the sound produced?
2.73e-2 m
A thin ring has a mass of 3 kg. It has a radius of 5m. The angular speed increases from 4 to 5 rad/s. What is the change in rotational kinetic energy?
A. 187.5 J
B. 337.5 J
C. 600.0 J
D. 937.5 J
B
A solid wheel starts from rest and undergoes a constant angular acceleration of 3.5 rad/s2. After 6.0 seconds what is the wheel's final angular velocity? How many radians has it rotated through in that time? If the wheel has a radius of 0.40m what is the linear (tangential) acceleration of a point on its edge?
21 rad/s
63 rad
1.4 m/s2
What force must be exerted on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the wheel cylinder? The pedal cylinder has a 2.00-cm diameter and the wheel has a 24.0-cm diameter.
(Textbook Problem)
136.11 N
A rotating disk has an angular acceleration of 5.0 rad/s2. If the disk starts with an angular velocity of 4.0 rad/s, what is the angular displacement after 25 seconds.
1662.5 rad
A 1.5 kg block is connected to a horizontal spring with spring constant of 250N/m. The block is pulled slightly from its equilibrium position and then released, allowing it to oscillate back and forth on a frictionless surface. What is the frequency of the oscillation?
2.06 Hz
If a mass on a pendulum is quadrupled, what happens to the period?
A. Halves
B. Doubles
C. Quadruples
D. Stays the same
D
A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. Repeat the calculation for the same ball if it slides up the hill without rolling.
5.44m
3.27m
A beaver makes a dam to block a river. (assume the beaver is a really good builder and made the side of the dam that faces the water completely flat)
The dam has a width of 10m and a height of 5m. If the water goes all the way up the side of the dam, what is the pressure at the bottom. What is the average pressure on the dam? What is the average force exerted on the dam? rho water = 1000 kg/m3
bottom pressure: 4.9e4 Pa
Average pressure: 2.45e4 Pa
Average force: 1.23e6 N
A liquid with density 950 kg/m3 flows through a horizontal pipeline in an industrial cooling system. At point A, the pipe has a diameter of 3.0cm, the fluid speed is 2.5 m/s, and the pressure is 30e5 Pa. Farther along the pipe, at point B, the diameter decreases to 1.5cm. Find the following at point B:
a. the speed of the fluid
b. the pressure of the fluid
a. 10 m/s
b. 2.96e6 Pa
A transverse wave traveling along a stretched rope is described by the equation y= (0.03m)sin(πx +6t) where x and y are measured in meters and t is measured in seconds. What is the wavelength of this wave?
2.0 m
A vertical wall holds water to a depth of 6 m. What is the average pressure on the wall? (rho water= 1000 kg/m3)
A. 29,400 Pa
B. 19,600 Pa
C. 58,800 Pa
D. 9,800 Pa
A
Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
(Textbook problem)
25.3 rpm
A diver is at the bottom of a tank of water. He is standing on a scale. If the man's normal weight force is 710N out of the water, and a density of 1300 kg/m3, what does the scale read? (answer in unit of kg) (rho water = 1000kg/m3)
16.7 kg
A rotating solid disk has an angular momentum of 100 kg m2/s. It has a mass of 10kg and a radius of 0.5m. What is rotational kinetic energy of the rotating disk?
4000 J
A 800g cart is attached to a horizontal spring with a spring constant of 200n/m. The cart is pulled slightly from the equilibrium and released so it oscillates without friction.
What is the period of the oscillation?
0.397 s
At what position in simple harmonic motion is speed maximum?
A. Maximum displacement
B. Half amplitude
C. Equilibrium position
D. Depends on mass
C