Prelim 2 & Solutions - 1.(5 points) A block of mass m...

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1.(5 points) A block of mass m is initially traveling with a velocity v 0 up an inclined plane set at an angle θ to the horizontal. The coefficient of friction is equal to μ and gravity is acting. What distance, d, will the block travel along the slope before it stops? 2. (5 points) Two objects are traveling on a collision course as shown, moving in a horizontal direction. The picture is drawn in thecenter-of-mass frame. The velocity of the first object measured relative to the center of mass is v 1 . Whatis the velocity v 2 of the second object relative to the center of mass? Write this velocity in terms of m 1 , m 2 , and v 1. Specify the magnitude and direction. Explain.
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3. (5 points) At time t = 0, a ball of mass m is thrown horizontally with velocity V 0 from a point P, as shown below. . The ball goes past the edge of a cliff and falls under the influence of gravity. Ignore air resistance. Determine an expression for the angular momentum of the ball as a function of time, L(t), relative to point P, including both magnitude and direction. Explain. 4. (5 points) Each of the wheels below has a total mass of 1 kg, they are initially at rest, and forces are applied as shown. Assume that the axles and spokes are massless, so that all of the mass of the wheels is in their outer rims. In order to impart identical angular accelerations, how large must F 2 be? Explain.
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5. (5 points) A force with magnitude F Newtons is applied to an object at point P, in the direction shown. What is the torque relative to point 0 due to this force? Specify both the magnitude and the direction. Explain.
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m slides with speed v 0 along a horizontal frictionless surface towards an identical block B, initially at rest, that is attached to an ideal spring of spring constant k and negligible mass. Both blocks are free to slide along the surface. While block A is in contact with the spring, what is the spring's greatest amount of compression Δ x max ? Your answer may contain
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Prelim 2 & Solutions - 1.(5 points) A block of mass m...

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