Physics 213 Final Exam 20 points each Dec. 10, 1997

1. a)What is the value of the ratio of circumference to diameter of any circle ?

b) Write down the meaning of this value.

c) If the circumference of a circle is increased by 8.4¹ cm , by how much is the radius increased?

2. The velocity-time graph of an object is shown below.

a) Find the total distance traveled by the object. Show your work.

b) Find the total displacement of the object.

3. A rope with tension T gently pulls a cart, initially at rest along a horizontal frictionless surface. At the instant the carts speed becomes 20 m/s, the tension is reduced T/2.

a) Draw a velocity vs time curve and a motion diagram for the cart.

b) Explain very carefully in complete sentences what happens to the speed of the cart.

4. 1. A hot air balloon is traveling vertically upward at a constant speed of 5.00 m/s. When it is 30 m above the ground, a package is dropped from the balloon. Analyze the motion of the package.

Motion Graphs: Motion Diagram & ERF Motion information: Events?

6.

8. A daredevil gazelle leaps off a 50 m cliff at 100 m/s at an angle of 30o with the horizontal. How far from the base of the cliff does she strike the ground? Assume g = 10 m/s2.

9. A 140 kg astronaut is standing on the extreme edge of a stationary 1000 kg space platform. He walks at a constant speed of 5 m/s, with respect to the fixed stars, toward the other edge of the platform. (He wears special magnetic shoes which allow him to walk along the metal platform.) As he walks, the platform moves through space. (Find the final speed of the platform relative to the fixed stars.)

10. A car of mass m passes over a bump in a road that follows the arc of a circle of radius R as in the figure below. A free body diagram ought to be worth a few points. Be careful with your frame of reference. Must I mention rain, doors, bedrooms etc.?

(a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at a speed v?

(b) What is the maximum speed the car can have as it passes this point before losing contact with the road.

20 Points Bonus!!

A child's toy consist of a piece of plastic attached to a spring (Figure P8.48). The spring is compressed 2.0 cm, and the toy is released. If the mass of the toy is 100 g and it rises to a maximum height of 60 cm, estimate the force constant of the spring.