1 PPMF102 – Lecture 2 Work & Energy

2 Work = force x displacement x cos  Work = force x displacement x cos  W = Fs cos  W = Fs cos  Scalar quantity Scalar quantity Unit: Joule (J) Unit: Joule (J) 1 J = 1 Nm 1 J = 1 Nm Energy is the ability to do work. Energy is the ability to do work. Energy is conserved. Energy is conserved. Can be in many forms. Can be in many forms. Scalar quantity. Scalar quantity. Unit: Joule (J) Unit: Joule (J) 1 J = 1 Nm 1 J = 1 Nm

W = Fs cos  W = Fs cos  Force can be exerted on an object yet no work is done. Force can be exerted on an object yet no work is done. Both force and displacement are needed to do work. Both force and displacement are needed to do work. W = 0 when  = 90  W = 0 when  = 90  No work is done by the person in moving the grocery bag horizontally at constant velocity. No work is done by the person in moving the grocery bag horizontally at constant velocity. 3

4 Eg. 1 Work done by a pile driver How much work is done by the gravitational force when a 240-kg pile driver falls 2.60 m? How much work is done by the gravitational force when a 240-kg pile driver falls 2.60 m?

5 Kinetic Energy Kinetic energy is the energy of motion. Kinetic energy is the energy of motion. A body that moves has kinetic energy, while a body that stays at rest has no kinetic energy. A body that moves has kinetic energy, while a body that stays at rest has no kinetic energy. A body of mass m that moves with velocity v has the following kinetic energy: A body of mass m that moves with velocity v has the following kinetic energy: K = ½ mv 2 K = ½ mv 2

6 Kinetic energy & work Work done on a body is equal to the change in its kinetic energy – work kinetic energy theorem. Work done on a body is equal to the change in its kinetic energy – work kinetic energy theorem. Illustration: Illustration: A body moves with an initial velocity v 1. When work (W) is done on the body its velocity changes to v 2. A body moves with an initial velocity v 1. When work (W) is done on the body its velocity changes to v 2. W = ½ mv 2 2 – ½ mv 1 2 W = ½ mv 2 2 – ½ mv 1 2

7 Eg. 4 Work to accelerate a car How much work is required to accelerate a 1000-kg car from 20 m/s to 30 m/s? How much work is required to accelerate a 1000-kg car from 20 m/s to 30 m/s?

8 Potential Energy Energy associated with the position or configuration of an object. Energy associated with the position or configuration of an object. Energy associated with the position of an object is called gravitational potential energy. Energy associated with the position of an object is called gravitational potential energy. Energy associated with the configuration of a spring is called elastic potential energy. Energy associated with the configuration of a spring is called elastic potential energy.

9 Gravitational Potential Energy U = mgh U = mgh  U = mgh 2 – mgh 1  U = mgh 2 – mgh 1 W =  U W =  U

10 Elastic potential energy U = ½ kx 2 U = ½ kx 2

11 Conservation of Mechanical Energy If only mechanical forces are doing work, the total mechanical energy of a system stays constant. If only mechanical forces are doing work, the total mechanical energy of a system stays constant. E 1 = E 2 E 1 = E 2 K 1 + U 1 = K 2 + U 2 K 1 + U 1 = K 2 + U 2 ½ mv mgh 1 = ½ mv mgh 2 ½ mv mgh 1 = ½ mv mgh 2

12 Energy interchange between U and K: Energy interchange between U and K: A free falling body U changes to K U changes to K

Eg. 5 Falling rock A rock of mass 1.5 kg is dropped from a height of 2.8 m. Determine the velocity of the rock when it is 1.0 m from the floor. 13

14 Energy interchange between K & U: simple pendulum At 1: E 1 = U 1 + K 1 At 1: E 1 = U 1 + K 1 Since K 1 = 0,  E 1 = U 1 At 2: E 2 = U 2 + K 2 At 2: E 2 = U 2 + K 2 At 3: E 3 = U 3 + K 3 At 3: E 3 = U 3 + K 3 Since U 3 = 0,  E 3 = K 3 At 4: E 4 = U 4 + K 4 At 4: E 4 = U 4 + K 4 At 5: E 5 = U 5 + K 5 At 5: E 5 = U 5 + K 5 Since K 5 = 0,  E 5 = U 5 Since K 5 = 0,  E 5 = U 5 E 1 = E 2 = E 3 = E 4 = E 5 = E E = Total energy Total energy remains constant.

15 Eg. 6 Velocity of pendulum bob A pendulum bob is tied to a string of length 50 cm. If A is the highest position of the bob, what is its velocity at position B which is 5 cm from its lowest position C? A pendulum bob is tied to a string of length 50 cm. If A is the highest position of the bob, what is its velocity at position B which is 5 cm from its lowest position C? 5 cm 8 cm A B C