exam02_f05_practice_sol - Physics 8.01T MASSACHUSETTS...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2005 Practice Problems Exam 2 Solutions Problem 1 Mechanical Energy and Simple Harmonic Motion Consider an ideal spring that has an unstretched length 0 l . Assume the spring has a constant k . Suppose the spring is attached to an cart of mass m that lies on a frictionless plane that is inclined by an angle θ from the horizontal. Let g denote the gravitational constant. The given quantities in this problem are 0 l , m , k , , and g . a) The spring stretches slightly to a new length 0 ll > to hold the cart in equilibrium. Find the length l in terms of the given quantities. b) Now move the cart up along the ramp so that the spring is compressed a distance x from the unstretched length 0 l . Then the cart is released from rest. What is the velocity of the cart when the spring has first returned to its unstretched length 0 l ? c) What is the period of oscillation of the cart?
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4 Problem 2: Work, Mechanical Energy, Simple Harmonic Motion A block of mass m slides along a horizontal table with speed v 0 . At x = 0 it hits a spring with spring constant k and begins to experience a friction force. The coefficient of friction is variable and is given by μ = bx , where b is a constant. Find the loss in mechanical energy when the block first momentarily comes to rest.
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5 Problem 3 Mechanical Energy and Work You are a member of an alpine rescue team situated at the bottom of an incline and must project a box of supplies up a slope, inclined at a constant angle θ with respect to the horizontal, so that it reaches a stranded skier. The skier is a vertical distance h above the bottom of the incline. The box has mass m . The incline is slippery, but there is some friction present, with kinetic friction coefficient k μ . Calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.
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6 Problem 4: Work, Energy, and the Harmonic Oscillator Experiment A cart of mass m moves down a plane inclined at angle θ from the horizontal. An ideal spring is placed at the bottom of the inclined plane. The cart collides with the spring and moves back up the incline plane. A motion sensor is placed at the top of the inclined plane that measures the position of one end of the cart. The coefficient of kinetic friction between the cart and the surface
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exam02_f05_practice_sol - Physics 8.01T MASSACHUSETTS...

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