Classroom Examples for Test 3

Example #1
A 0.14 kg baseball with an initial speed of 28 m/s rebounds with a speed of 34 m/s after being struck with a bat. a) If the duration of contact between ball and bat was 2.1 ms, what was the average force on the ball? b) What was the average force on the bat?

Example #2
Leslie is rolling along on her 4.0 kg skateboard with a constant speed of 3.0 m/s when she jumps off the back and continues forward with a velocity of 2.0 m/s relative to the ground. This causes the skateboard to go flying forward with a speed of 15.5 m/s relative to the ground. What is Leslie’s mass?

Example #3
A 12.0 g bullet is fired horizontally into a 101 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having a spring constant 152 N/m. The bullet becomes embedded in the block. If the initial speed of the bullet is 273 m/s, by how much does the bullet-block system compress?

Example #4
A 2020 kg car moving east at 10.0 m/s collides with a 3010 kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 40.0^o north of east and at a speed of 5.22 m/s. Find the speed of the 3010 kg car before the collision.

Example #5
Two air track gliders of equal mass are initially moving in the same direction along a straight line. The rearmost glider has an initial speed of 3.0 m/s and the forward glider has a speed of 2.0 m/s. If the collision is elastic, what are the speeds and directions of the gliders after the collision?

Example #6
(#83, page 294) Find the center of mass of a water molecule. The mass of a hydrogen atom is 1.0 u, and the mass of an oxygen atom is 16 u. Use the center of the oxygen atom as the origin of your coordinate system.


Example #7
The angular velocity of the rotor in a centrifuge increases from 420 rad/s to 1420 rad/s in a time of 5.00s. a) What is the magnitude of the angular acceleration?b) What is the angle through which the rotor turns?

Example #8
Discuss throwers often warm up by standing with both feet flat on the ground and throwing the discus with a twisting motion of their bodies. Starting from rest, the thrower accelerates the discus to a final angular velocity of 15.0 rad/s in a time of 0.270 s before releasing it. During the acceleration, the discus moves on a circular arc of radius 0.810m. Find the magnitude of the total acceleration of the discus just before it is released.

Example #9
The Atwood’s machine below consists of masses m₁ = 1.35 kg and m₂ = 1.15 kg and a solid pulley with a diameter of 6.70 cm and a mass
m_p = 0.546 kg. When released from rest, what is the speed of the heavier mass after it has fallen a distance of h = 1.45 m?
Treat the pulley as a uniform disk.

Example #10
The force below creates a torque of magnitude 45 Nm on the bar. Using the data in the drawing, determine the magnitude of the force F.


Exmaple #11
(#12 page 367) When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius of 6.0 cm and a mass of 17 g, what is the torque exerted on it? Treat the CD as a uniform disk.

Exmaple #12
(#26 page 367) To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50 m apart. If the left scale reads 290 N, and the right scale reads 122 N, find a) the student’s mass and b) the distance from the student’s head to her center of mass.

Example #13
A uniform board is leaning against a smooth vertical wall. The board is at an angle q above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.650. Find the smallest value for the angle q, such that the lower end of the board does not slide along the ground.

Example #14
A solid, frictionless cylindrical reel of mass m₁ = 3.00 kg and radius r = 0.440 m is used to draw water from a well. A bucket of m₂ = 2.00 kg is attached to a cord that is wrapped around the cylinder. If the bucket starts from rest at the top of the well and falls for 3.00 s before hitting the water, how far does it fall?

Example #15
A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 201 kg and a radius of 1.8 m. A 36 kg child rides at the center of the merry-go-round while a playmate sets it turning at 0.25 rev/s. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning?

Example #16
A metal block is hung from a spring that obeys Hooke’s law. When the block is pulled down 12 cm from the equilibrium position and released from rest, it oscillates with a period of 0.75 s. What is the position of the block 0.28 s after it is released?

Example #17
(#29, page 446) The pistons in an internal combustion engine undergo a motion that is approximately simple harmonic. If the amplitude of motion is 3.5 cm, and the engine runs at 1700 rev/min, find a) the maximum acceleration of the pistons and b) their maximum speed?

Example #18
(#49, page 448) A 1.8 kg mass attached to a spring oscillates with an amplitude of 7.1 cm and a frequency of 2.6 Hz. What is its energy of motion?

Example #19
A 0.75 m string is stretched so the tension in 2.3 N. A transverse wave with a frequency of 150 Hz and a wavelength of 0.40 m travels on the string. What is the mass of the string?

Example #20
A rocket in a fireworks display explodes high in the air. The sound spreads out uniformly in all directions. The intensity of the sound is 2.0x10^-6 W/m² at a distance of 120 m from the explosion. Find the distance from the source at which the intensity is 0.80x10^-6 W/m².

Example #21
The bellow of a territorial bull hippopotamus has been measured at 115 dB above the threshold of hearing. What is the sound intensity?

Example #22
At a football game, a stationary spectator is watching the halftime show. A trumpet player in the band is playing a 784 Hz tone while marching directly toward the spectator at a speed of 0.83 m/s. On a day when the speed of sound is 343 m/s, what frequency does the spectator hear?

Example #23
A trailer truck traveling east at 28 m/s sounds a 1.0x10³ Hz horn. What frequency is heard by an approaching driver headed west at 38 m/s?