Aim: How do we explain conservation of energy?

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

Conservation of Energy

Thought Question 1 A coconut is thrown off the edge of a cliff with an initial speed vi = 8 m/s. Rank the following launch directions according to (a) greatest initial kinetic energy and (b) greatest final kinetic energy upon hitting the ground. Coconut is thrown vertically upwards Coconut is thrown upwards at an angle of 45 degrees Coconut is thrown horizontally Coconut is thrown vertically downwards Coconut is thrown downwards at an angle of 45 degrees All have the same initial kinetic energy All have the same final kinetic energy

Conservation of Energy Example A rollercoaster car of a mass of 100 kg starts at rest on point A. Find the potential energy and kinetic energy of the rollercoaster at points A,B,C, and E.

Isolated System Problem 1 A particle of mass 0.500 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

Problem 1

Problem 1

Thought Question 2 A small stationary block is released from rest at the top of a 3m tall frictionless ramp. Which hill is the first hill that the block cannot cross? Hill number 4 b)What does the block do after failing to cross the hill? It will oscillate between the point where it stops and the point where it was released from c)On which hilltop is the centripetal acceleration the greatest? Hill number 1 because this is where the cart is fastest d)On which hilltop is the normal force the least? Hill number 1

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.

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 0.005 kg? a) v= √7gR b)v=√(3gR) c)0.1 N down

Problem 2

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

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

Problem 3

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.

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

Problem 4