Physics 170 - Mechanics Lecture 16 Work & Energy @ home: • Examples from the book: • 6.1 pag. 178, 6.2 pag. 180, 6.3 and 6.4 pag. 184, 6.5 pag. 186, • read figure 6.4 pag. 179, • problem solving strategy pag. 183. • ex. 6.6 and 6.7 pag. 189, 190; • ex. 6.8 pag. 192; • ex. 6.9 and 6.10 pag 196. Kinetic Energy & The Work-Energy Theorem

After algebraic manipulations of the equations of motion, we find:

Therefore, we define the kinetic energy: Kinetic Energy & The Work-Energy Theorem

Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy. Example: A Dogsled Race

You pull a sled (mass 80 kg) with a force of 180 N at 40° above the horizontal. The sled moves Δx = 5.0 m, starting from rest. Assume that there is no friction.

(a) Find the work you do.

(b) Find the final speed of your sled. Example: Work and Kinetic Energy in a Rocket Launch

A 150,000 kg rocket is launched straight up. The rocket engine generates a thrust of 4.0 106 N.

What is the rocket’s speed at a height of 500 m? (Ignore air resistance and mass loss due to burned fuel.) Power Power is a measure of the rate at which work is done:

James Watt (1736-1819) SI power unit: 1 J/s = 1 watt = 1 W

1 horsepower = 1 hp = 746 W Power Power and Velocity

d d

d

Power is the rate of energy flow.

(horsepower) 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: Example: Pushing a Puck

A 500 g ice hockey puck slides across frictionless ice with an initial speed of 2.0 m/s. A compressed air gun is used to exert a continuous force of 1.0 N on the puck to slow it down as it moves 0.50 m. v1 The air gun is aimed at the front edge of v1 the puck, with the compressed air flow 30o below the horizontal. What is the puck’s final speed? Example: Work on an Electron

In a television picture tube, electrons are accelerated by an electron gun. The force that accelerates the electron is an electric force due to the electric field in the gun. An electron is accelerated from rest by an electron gun to an energy of 2.5 keV (2,500 eV) over a distance of 2.5 cm. (1 eV = 1.60 x 10-19 J)

Find the force on the electron, assuming that it is constant and in the direction of the electron’s motion. Example: Work Done on a Block by a 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 = x1 = -5.0 cm

to its equilibrium position of x = x2 = 0 cm.

(b) Find the speed of the block at x2 = 0 cm. Example: 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? Problem Solving Strategy

Picture: The way you choose the +y direction or the +x direction can help you to easily solve a problem that involves work and kinetic energy.

Solve: 1. Draw the particle first at its initial position and second at its final position. For convenience, the object can be represented as a dot or box. Label the initial and final positions of the object. 2. Put one or more coordinate axes on the drawing. 3. Draw arrows for the initial and final velocities, and label them appropriately. 4. On the initial-position drawing of the particle, place a labeled vector for each force acting on it. 5. Calculate the total work done on the particle by the forces and equate this total to the change in the particle’s kinetic energy.

Check: Make sure you pay attention to negative signs during your calculations. For example, values for work done can be positive or negative, depending on the direction of the displacement relative to the direction of the force. Kinetic energy values, however, are always positive.