1. An object of mass m rests at the top of a smooth slope of height h, length L and angle 0. The coefficient of kinetic friction Hx is small enough that once the object is given a small push, it will slide down the slope. a. Sketch the physical situation, choose a coordinate system and draw a free body diagram for the object. List the knowns and unknowns. (Hint: choosing a coordinate system that is aligned with the motion of the object will make calculations easier.) b. Write down Newton's Second Law for the y motion of the object. Using this determine an expression for the magnitude of the normal force. c. Write down Newton's Second law for the x motion of the object. Using this, and your result from part b, determine an expression for the acceleration of the object down the slope. d. Using your knowledge of the kinematic equations, determine an expression for the object's speed at the bottom of the hill. This should be in terms of some of all of given known variables m, h, L, g, 0 and µk. e. Suppose a snowboarder slides down a ski slope of height h 100 m and the coefficient of kinetic friction between their board and the snow is 12.0 m, length L = Hx= 0.07. What is the snowboarder's speed at the bottom of the hill? Suppose this snowboarder has a little sister who is half the mass of her older sibling. What is the little sister's speed at the bottom of the hill? Does your result make sense? Explain.

1. An object of mass m rests at the top of a smooth slope of height h, length L and angle 0. The coefficient of kinetic friction Hx is small enough that once the object is given a small push, it will slide down the slope. a. Sketch the physical situation, choose a coordinate system and draw a free body diagram for the object. List the knowns and unknowns. (Hint: choosing a coordinate system that is aligned with the motion of the object will make calculations easier.) b. Write down Newton's Second Law for the y motion of the object. Using this determine an expression for the magnitude of the normal force. c. Write down Newton's Second law for the x motion of the object. Using this, and your result from part b, determine an expression for the acceleration of the object down the slope. d. Using your knowledge of the kinematic equations, determine an expression for the object's speed at the bottom of the hill. This should be in terms of some of all of given known variables m, h, L, g, 0 and µk. e. Suppose a snowboarder slides down a ski slope of height h 100 m and the coefficient of kinetic friction between their board and the snow is 12.0 m, length L = Hx= 0.07. What is the snowboarder's speed at the bottom of the hill? Suppose this snowboarder has a little sister who is half the mass of her older sibling. What is the little sister's speed at the bottom of the hill? Does your result make sense? Explain.