Physics 201 MWF10:20 Fall 2003 (Ford)
Exam III Chapts 8--11 Cutnell and Johnson 6th ed
Multiple choice questions. Circle the correct answer. No work need be shown and no partial credit will be given.
(5 pts) 1. A uniform solid sphere has mass 5.0 kg and radius 0.10 m. Its moment of inertia for an axis through its center is (2/5)mr2. The sphere is rolling without slipping on a horizontal surface and its center of mass has a translational speed of 4.0 m/s. What is the total kinetic energy of the sphere?
(a) 16 J
(b) 36 J
(c) 40 J
(d) 56 J
(e) 90 J
(f) 126 J
(g) none of the above
(5 pts) 2. A rod is rotating about an axis at one end with an angular speed of 5.0 rad/s. A large bug is standing on the rod at the other end, and the moment of inertia of the system (rod plus bug) about the rotation axis is 30 kg·m2. The bug then crawls to the axis end of the rod and the moment of inertia of the system becomes 7.5 kg·m2. What is the angular speed of the rod when the bug is at this new position on the rod?
(a) 10 rad/s
(b) 20 rad/s
(c) 30 rad/s
(d) 40 rad/s
(e) 50 rad/s
(f) none of the above
(5 pts) 3. A wheel in the shape of a disk with radius 0.50 m is rotating with constant angular velocity about an axis through its center. The centripetal acceleration of a point on the rim of the wheel is 8.0 m/s2. How long does it take the wheel to make one revolution?
(a) (2
/3) s
(b) (2/4) s
(c) (2/5) s
(d) (2/6) s
(e) none of the above
(4pts) 4. A block attached to a horizontal spring is moving in simple harmonic motion with an amplitude of 0.20 m and a period of 0.60 s. If the amplitude of the motion is increased to 0.40 m, what then is the period of the motion?
(a) 0.3 s
(b) 0.6 s
(c) 1.2 s
(d) 2.4 s
(e) none of the above
(4 pts) 5. An ice cube (density 910 kg/m3) is floating in a glass of water. When the ice cube melts, does the level of water in the glass
(a) rise
(b) fall
(c) stay the same
On the following problems show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.
(18 pts) 6. A small block with mass 0.50 kg is attached to a horizontal spring that has spring constant 400 N/m. The block is moving in simple harmonic motion on a horizontal frictionless surface. During the motion of the block, when it is displaced 0.10 m to the right of its equilibrium position the speed of the block is 3.0 m/s.
a) What is the amplitude of the simple harmonic motion?
Ans.______________
b) What is the maximum speed of the block during its motion?
Ans._____________
c) What is the magnitude of the maximum force exerted by the spring on the block during its motion?
Ans. _____________
(18 pts) 7. A wheel with radius 0.30 m is pivoted about a vertical axis through its center. A constant force F = 20 N is applied tangential to the rim of the wheel. Starting from rest, the wheel turns through 4.0 rev in 5.0 s. Calculate the moment of inertia of the wheel.
Ans. ___________
(21 pts) 8. One end of a uniform board that has mass 20 kg is attached to a wall by a frictionless hinge. The board is held stationary at an angle of 53° above the horizontal by a horizontal rope. One end of the rope is attached to the upper end of the board and the other end of the rope is attached to the wall.
a) What is the tension in the rope?
Ans. _________________
b) What are the magnitude and direction of the resultant force exerted by the hinge on the board? Specify the direction by giving the angle of the resultant force relative to the horizontal.
Ans. magnitude ________________
angle ____________________
(20 pts) 9. A rock is suspended from one end of a light string.
a) When the rock is in air, the tension in the string is 40 N. When the rock is completely immersed in oil (density = 800 kg/m3), the tension in the string is 30 N. What is the volume of the rock?
Ans. ______________
b) What is the tension in the string when the rock is completely immersed in water (density = 1000 kg/m3)?
Ans. ________________