AP Energy Conservation Note Problems

1 A bicyclist is coasting on level ground at 32.25 m/s. The bicyclist coasts up an incline and grabs an overhanging tree limb. How fast is the bicyclist traveling when he grabs the limb?

2 What is the velocity of the dropped package after falling 1500 m?

3 A flying trapeze artist starts her swing from rest.

 (a) How fast is she traveling at the lowest point? (b) How fast is she traveling 3.33 meters below the starting height? (c) If she drops from the lowest point of her swinging motion, then how far horizontally will she before reaching a velocity of 15.22 m/s? (d) How fast will she be traveling when she hits the net below, 22.5 below the starting height? (e) In a different acrobatic stunt, the trapeze artist is traveling 2.987 m/s when she is 1.322 m above her starting height. What was her initial velocity?

Below is a ride at Dr. Seuss’s amusement park in “Whoville.” Based on the information diagramed below. Answer questions 4 - 9.

4 What is the speed of the car at the top of the hill?
5 What is the spring’s spring constant?
6 What is the speed of the car when the spring is compressed 5 meters?
7 At which compression distance of the spring is the speed of the car half of what was at the instant it hit the spring?
8 At which compression distance of the spring is the speed of the car half of what it was at the very beginning of the ride?
9 Suppose, by some weird quirk of Seuss’ Science, the spring bounces the car with 3 times the total energy it hit the spring with. What is the new speed of the coaster when it leaves the spring?

Wyle E. Coyote is still trying to catch that road runner -when will he learn? As part of this new ACME trap he throws a ball down on a spring as shown below. Use this description and diagram for questions 10 and 11.

10 What is the velocity of the ball the instant it makes contact with the spring?
11 What is the spring’s spring constant?

12 A 120 N sled & rider is pulled by a 200 N for 100 m. The force acts at a 60° angle with the ground. How much work is done by the applied force?

13

The above car is traveling at 35 m/s when the driver decides to skid to a stop. For some weird reason, the coefficient of friction keeps changing for the car.

(a) What is the speed of the car after skidding 10 meters?
(b) What is the speed of the car after 20 meters if the 5000N propels the car?
(c) How much more distance is required for the car to come to rest?
14. The spring is compressed 25.0 meters from equilibrum. What is the spring’s spring constant if the glider is leave the launch tower at exactly 100 m/s?

15. The spring is compressed 25 meters meters from equilibrum. What is the spring’s spring constant if the glider is leave the launch tower at exactly 100 m/s?

16. The plane below is a spring launched jet. The engine exerts a constant force of 45 550N across the 20.0 m length of the tower. Considering the quantities shown below, calculate the launch speed of the jet if its engines fire the whole time and the spring has a force constant of 4100 N/m. The jet starts from rest. The spring is compressed 20.0 m from equilibrium at launch.

In class example problems
N1 Ena G. is having fun on her home made swing. Find the speed at the lowest point in the swinging motion.

N2 Ena G. (44kg) is trying to invent a new ride. She swings from a position 21m above the ground and lands into a massless wagon 7 m above the ground. The wagon rolls for 11 meters until it comes to a rest. What is the magnitude of the stopping force?

N3 Ena G. (44kg) is still trying to invent a new ride. She swings from a position 21m above the ground and lands into a massless wagon 7 m above the ground. The wagon rolls until it comes to a rest 4m above the left end of the ramp. the same frictional force stops the wagon. How far along the incline did the wagon travel?

N4

This is Ena G.'s last attempt at backyard amusement park ride design. When Ena G., 40.0 kg, is at the highest point on the left, she is 8.00 meters above the spring. The wagon is a special massless physics wagon.

(a) How far along the incline is the spring compressed?

(b) How much force does the spring exert at maximum compression?

(c) What average force does the spring exert across this compression distance?

(d) What average acceleration does Ena G. Experience during the spring's compression?

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)