Fundamentals 10

Question 1

An object hangs on a vertical spring. Let the position where the object hangs in equilibrium be the zero of potential energy. What is the formula for the potential energy of the spring-object-earth system? Define each variable briefly.

Answer 1

(1/2)kx^2, where k is the spring constant and x is the distance from the place where the object hangs in equilibrium. (For a vertical spring, if you define x=0 as in this problem, you can consider all potential energy, including gravitational and spring, to be encompassed in this single formula.)

Question 2

Consider a wooden block on a wooden surface. Which is larger, the coefficient of static friction between the surfaces, or the coefficient of kinetic friction?

Answer 2

the coefficient of static friction.

Question 3

An object slides up an incline which sits at an angle θ above the horizontal. What is the formula for the component of the object’s weight that acts perpendicular to the incline?

Answer 3

mgcos(theta)

Question 4

Under what conditions does an object experience balanced forces?

Answer 4

when it moves in a straight line at a constant speed.

Question 5

Sophia pushes a ball to the right. After she lets go, the ball rolls right and slows down. While the ball slows down, what is the direction of the force applied by Sophia to the ball?

Answer 5

no direction; no force. (Sophia is no longer touching the ball while it slows down. In P1, all forces other than gravity require contact in order to exist.)

Question 6

What is the weight of a 90 kg person on earth?

Answer 6

900 N

Question 7

Write the kinematics equation for angular displacement under constant angular acceleration.

Answer 7

angular displacement = (w0)t + (1/2)(alpha)t^2. (Angular kinematics equations are identical in form to linear kinematics equations.)

Question 8

A block which weighs 100 N is attached to a string, which pulls vertically upward. The block moves upward and slows down. Is the tension in the string greater than, less than, or equal to 100 N?

Answer 8

less than. (Acceleration is downward, so the unbalanced force is downward, so the weight is greater than the tension.)

Question 9

What are the units of the coefficient of static friction?

Answer 9

there are no units.

Question 10

wo 1 kg carts are connected by a compressed spring, and are initially at rest. The spring uncoils, causing the carts to move in opposite directions, each with 1 m/s of speed. What is the total momentum of the two-cart system after the spring uncoils?

Answer 10

zero. (Momentums in opposite directions subtract.)