Work-2 & Power

Work and Area If the force is constant, we can graphically interpret the work done ( W = F d ) as the area of a rectangle F tall and d wide:

Work Done by a Variable Force If the force takes on several successive constant values we can add adjacent rectangles:

Work Done by a Variable Force We can then approximate a continuously varying force by a succession of constant values.

Work Done by a Varying Force A force F x varies with x as shown. Find the work done by the force on a particle as the particle moves from x = 0.0 m to x = 6.0 m.

Spring ACT 1 The force vs. displacement curves of three springs are measured. Which spring has the largest spring constant? a) Spring 1 b) Spring 2 c) Spring 3 d) They are all the same

Work and Springs The force needed to stretch a spring an amount x is F = kx. Therefore, the work done in stretching the spring is (7-8)

Spring ACT 2 A spring-loaded gun shoots a plastic ball with a speed of 4.0 m/s. If the spring is compressed twice as far, what is the ball’s speed? a) 2.0 m/s b) 4.0 m/s c) 8.0 m/s d) 16.0 m/s e) 32.0 m/s 4.0 m/s

Work Done on Block by Spring A 4.0 kg block on a frictionless surface is attached to a horizontal spring with k = 400 N/m. The spring is initially compressed to 5.0 cm. (a) Find the work done on the block by the spring as the block moves from x = x 1 = -5.0 cm to its equilibrium position of x = x 2 = 0 cm. (b) Find the speed of the block at x 2 = 0 cm.

Power Power is a measure of the rate at which work is done: (7-10) SI power unit: 1 J/s = 1 watt = 1 W 1 horsepower = 1 hp = 746 W

Power

Power and Velocity If an object is moving at a constant speed in the presence of friction, gravity, air resistance, and so forth, the power exerted by the driving force can be written: (7-13)

The Power of a Motor A small motor is used to operate a lift that raises a load of bricks weighing 500 N to a height of 10 m in 20 s at constant speed. The lift weighs 300 N. What is the power output of the motor?