1. Aim: How do we explain conservation of energy?

2. High Road- Low Road
Predict which marble will travel faster. Will it be the marble which travels on the high road or the marble which travels along the low road? LOW ROAD because the object gains more kinetic energy and will move faster

3. Conservation of Energy

4. Isolated System Problem 1
A particle of mass kg is shot from P as shown below. The particle has an initial velocity vi with a horizontal velocity of 30 m/s. The particle rises to a maximum height of 20 m above P. Using conservation of energy,
The vertical component of vi
The work done by the gravitational force P to B
The horizontal and vertical components of the velocity vector when the particle reaches B

5. Problem 1

6. Problem 1

7. Problem-Loop Track
Identify what happens to each of the following as the bead travels along the track:
Gravitational Potential Energy, Kinetic Energy, Mechanical Energy
The gravitational potential energy decreases until point Q then increases until point A and then decreases after this.
The kinetic energy increases until point Q then decreases until point A and then increases after this.
The mechanical energy stays constant.

8. Isolated System Problem-Loop Track
A bead slides without friction around a loop-the-loop. The bead is released from a height h = 3.50R a) What is the speed of the object at the bottom of the track? b) What is the speed at point A? c) How large is the normal force on it at point A if it mass is kg?
a) v= √7gR b)v=√(3gR) c)0.1 N down

9. Problem 2

10. Pendulum Problem
Explain how the potential energy of the system changes as the pendulum bob swings from x to y to z.
Explain how the kinetic energy of the system changes as the pendulum bob swings from x to y to z.
Explain how the mechanical energy changes as the bob swings from x to y to z.
The potential decreases and then increases
The kinetic energy increases and then decreases
The mechanical energy doesn’t change

11. Isolated System Problem-Pendulum
A simple pendulum consists of a small object suspended by a string. The object is modeled as a particle. The string with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system oscillates by swinging back and forth in a vertical plane. If the string is 2 m long and makes an initial angle of 30 degrees with the vertical, calculate the speed of the particle
At the lowest point in its trajectory and
when the angle is 15 degrees.
a)2.29 m/s b)1.98 m/s

12. Problem 3

13. Isolated System Problem-Atwood Machine
Identify which form of energy this system has before mass 1 is released.
Identify which form of energy this system has after mass 2 hits the ground.

14. Isolated System Problem-Atwood Machine
Two objects are connected by a light string passing over a light, frictionless pulley. The 5 kg object is released from rest. Using conservation of energy,
determine the speed of the 3 kg object just as the 5 kg object hits the ground
Find the maximum height to which the 3 kg object rises.
a) 4.43 m/s b) 5 m

15. Problem 4