EXAM-3 PHYS 201 (Fall 2006), 10/31/06 Name: Signature: Duration: 75 minutes Show all your work for full/partial credit! Include the correct units in your final answers for full credit! Unless otherwise stated, quote your results in SI units!
1.) Short Answer Provide an answer for each question below. (24 pts.) (a) Name two types of forces that are conservative. (b) A figure skater is spinning with her arms stretched out. What happens when she brings her arms in toward her body? Explain the physics. (c) Two small 0.200 kg spheres (each of which you can regard as a point mass) are separated by 0.400 m. Calculate the moment of inertia of the system about an axis that is half the distance between the two spheres and perpendicular to a line connecting the two spheres. (d) Consider the same two spheres as in the previous question. Calculate the moment of inertia of the system about an axis that passes through both spheres. (e) Assume that four uniform objects have the same mass and diameter and are released simultaneously from rest at the same distance above the bottom of a hill and roll down without slipping. Which of these will be the first to reach the bottom of the hill? (Hint: the one with the greatest speed at the bottom.) A) solid sphere B) solid cylinder C) hollow cylinder D) thin-walled hollow cylinder (f) With the same conditions as in the last question, which of these will be the last to reach the bottom of the hill? A) solid sphere B) solid cylinder C) hollow cylinder D) thin-walled hollow cylinder
2.) Static Equilibrium (20 pts.) A uniform ladder 7.0 m long weighing 450 N rests with one end on the ground and the other end against a perfectly smooth vertical wall. The ladder rises 60 above the horizontal floor. A 750 N painter finds that she can climb 2.75 m up the ladder, measured along its length, before it begins to slip. (a) Draw the force diagram of the ladder (all forces acting on the ladder). (b) Set up the 3 equations for static equilibrium. (c) Calculate the force that the wall exerts on the ladder? (d) Find the coefficient of static friction µ s between the ladder and the floor? (Hint: Calculate the friction force and the normal force that the floor exerts on the ladder.)
3.) Ideal Spring (20 pts.) A 0.150 kg toy is undergoing simple harmonic motion on the end of a horizontal spring with force constant 300.0 N/m. When the object is 0.0120 m from its equilibrium position, it is observed to have a speed of 0.300 m/s. (a) What is the total mechanical energy of the object at any point in its motion? (b) What is the amplitude of its motion? (c) What is the maximum speed attained by the object during its motion? (d) Calculate the work done by the spring when it moves from its equilibrium position to its maximum displacement (or amplitude) A?
4.) Rotational Motion (18 pts.) A solid uniform spherical boulder rolls down a constant-slope hill, starting from rest at a height of 60.0 m above the bottom. The upper half of the hill is free of ice, so the boulder rolls without slipping. But the lower half of the hill is covered with perfectly smooth ice. (a) What types of energy does the boulder have at the top of the hill? (b) What types of energy does the boulder have half-way down the hill (right before it reaches the ice)? (c) How fast is the boulder moving when it reaches the part of the hill covered in ice? (d) As the boulder moves down the latter half of the hill, which part of the mechanical energy remains constant? (e) How fast is the boulder moving when it reaches the bottom of the hill?
5.) Rotational Kinematics (18 pts.) The front and rear sprockets on a bicycle have radii of 9.00 and 5.10 cm, respectively. The angular speed of the front sprocket is a constant 9.40 rad/s. (a) What is the linear speed of the chain as it moves between the sprockets? (b) What is the radial acceleration of the chain as it passes around the rear sprocket? (c) What is the angular speed of the rear sprocket? (d) How far does the bicycle travel in 5 minutes?
Name: Exam 3 - Version 1 No. 1 2 3 4 5 Sum Points