Work

SPH4C – April 2010

Work

• The energy transferred to an object by a force applied over a distance.

• W is the work done on the object,• F is the magnitude of the applied force in the

direction of the displacement,• Δd is the magnitude of the displacement.• Measured in Nm.

dFW

Was work done?

A student applies a force to a wall and becomes exhausted.

A book falls off a table and free falls to the ground.

A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed.

A rocket accelerates through space.

Negative Work

• If the force is opposite in direction to the displacement, the work is negative.

• When two forces are acting on an object, the total work done is the sum of the positive and negative values.

Negative Work

• Kinetic Friction

dFW K

Practice Page 135 Q1-4, 6

1. A farmer applies a constant horizontal force of magnitude 21 N on a wagon and moves it a horizontal distance of 3.2 m. Calculate the work done by the farmer on the wagon.

Practice Page 135 Q1-4, 6

2. Rearrange the equation W=FΔd to solve for (a) F and (b) Δd.

3. A truck does 3.2 kJ of work pulling horizontally on a car to move it 1.8 m horizontally in the direction of the force. Calculate the magnitude of the force.

Practice Page 135 Q1-4, 6

4. A store clerk moves a 4.4-kg box of soap at a constant velocity along a shelf by pushing it with a horizontal force of magnitude 8.1 N. The clerk does 5.9 J of work on the box.

a) How far did the box move?

Practice Page 135 Q1-4, 6

4b) What was the magnitude of the force of kinetic friction during the push?

4c) How much work was done by the force of kinetic friction on the box?

Work Done in Raising Objects

• The applied force of an object raised vertically under constant velocity is equal to the weight of the object.

Practice Page 136 Q8-9

A 150-g book is lifted from the floor to a shelf 2.0 m above. Calculate

a)the force needed to lift the book without acceleration

b)the work done by the force on the book to lift it up to the shelf

Practice Page 136 Q8-9

A world-champion weightlifter does 5.0 X 103 J of work in raising a weight from the floor to a height of 2.0 m. Calculate

a)the average force exerted to lift the weight

b)the mass of weight

Zero Work

• If the applied force and the displacement are perpendicular, no work is done by the applied force.

Practice Page 137 Q13

A nurse holding a 3.0-kg newborn baby at a height of 1.2 m above the floor carries the baby 15 m at constant velocity along a hospital corridor. How much work has the nurse done on the baby?

Work

Based on what you have learned so far, when is the work done on an object:

• positive?

• negative?

• zero?

Work and Springs

• When stretching an elastic material, the force changes as the displacement changes.

• The area under the line of the force-displacement graph yields the work done.

• The slope of the line gives the force constant of the spring k.• Representing the stiffness of the

spring.

x

Fk

Practice Page 137 Q15

• Calculate the work done in stretching the spring represented in the graph after it has stretched (a) 0.12 m and (b) 0.24 m.

Practice Page 138 Q3,5,7,8

3. A off-road dump truck can hold 325 t of gravel (1 t = 1000 kg). How much work must be done on a new load of gravel to raise it an average of 9.2 m into the truck? Express your answer in joules and megajoules.

Practice Page 138 Q3,5,7,8

5. The driver of a 1300-kg car suddenly slams on the brakes, causing the car to skid forward on the road. The coefficient of kinetic friction between the tires and the road is 0.97, and the car comes to a stop after travelling 27 m horizontally. Calculate the work done by the force of friction on the car during the skid.

Practice Page 138 Q3,5,7,8

7. A puck of mass 0.16 kg is sliding along the ice when it reaches a rough section where the coefficient of kinetic friction is 0.37. If -2.8 J of work is done on the puck to bring it to rest, how far does the puck slide before stopping?

Practice Page 138 Q3,5,7,8

8. Explain why the equation W=FΔd is not used to determine the work done by an applied force to stretch a spring.