PHYS 2211 Module 11 Self Assessment Practice Problems
Module 11 Self Assessment Practice Problems
A marble rolls down an incline at 30° from rest.
(a) What is its acceleration?
(b) How far does it go in 3.0 s?
Answer: (a) 3.5 m/s2 (b) 15.75 m
A bowling ball rolls up a ramp 0.5 m high without slipping to storage. It has an initial velocity of its center of mass of 3.0 m/s.
(a) What is its velocity at the top of the ramp?
(b) If the ramp is 1 m high does it make it to the top? Explain.
Answer: (a) 1.4 m/s (b) No
A bicycle racer is going downhill at 11.0 m/s when, to his horror, one of his 2.25-kg wheels comes off as he is 75.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0 cm in diameter and ignore the small mass of the spokes.
(a) How fast is the wheel moving when it reaches the foot of the hill if it rolled without slipping all the way down?
(b) How much total kinetic energy does the wheel have when it reaches the bottom of the hill?
Answer: (a) 29 m/s (b) 1925 J
A Formula One race car with mass 750.0 kg is speeding through a course in Monaco and enters a circular turn at 220.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 180 km/h also in the counterclockwise direction. If the radius of curvature of the first turn is 130.0 m and that of the second is 100.0 m, compare the angular momenta of the race car in each turn taken about the origin of the circular turn.
Answer: 5.96 x 106 kg•m2/s and 3.75 x 106 kg•m2/s
Suppose the particles in the figure have masses m1 = 0.10 kg, m2 = 0.20 kg, m3 = 0.30 kg, and m4 = 0.40 kg. The velocities of the particles are m/s, m/s, m/s, and .
(a) Use the right-hand rule to determine the directions of the angular momenta about the origin of the particles. The z-axis is out of the page.
(b) Calculate the angular momentum of each particle about the origin.
(c) What is the total angular momentum of the four-particle system about the origin?
A disk of mass 2.0 kg and radius 60 cm with a small mass of 0.05 kg attached at the edge is rotating at 2.0 rev/s. The small mass suddenly separates from the disk. What is the disk’s final rotation rate?
Answer: 2.1 rev/s
A small block on a frictionless, horizontal surface has a mass of 0.0250 kg. It is attached to a massless cord passing through a hole in the surface. The block is originally revolving at a distance of 0.300 m from the hole with an angular speed of 2.85 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.150 m. Model the block as a particle.
(a) Is the angular momentum of the block conserved? Why or why not?
(b) What is the new angular speed?
(c) Find the change in kinetic energy of the block.
The uniform seesaw is balanced at its center of mass, as seen in the figure. The smaller boy on the right has a mass of 40.0 kg. What is the mass of his friend?
Answer: 80 kg
A uniform 40.0-kg scaffold of length 6.0 m is supported by two light cables, as shown in the figure. An 80.0-kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.5 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the equipment.
Answer: 444.3 N, 888.5 N,, 16 kg
A uniform horizontal strut weighs 400.0 N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 200.0 N. The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.