Work, Power and Energy

What is the scientific definition of Work?

Work is done on an object when a force is exerted on the object and the object moves in the direction of the applied force

What are the three criteria that must be met for work to be done on an object?

1) A force must be exerted 2) The object must move as a result of the force 3) The object must move in the direction of the force

Why is work done when a force pushes a wheelbarrow across a road?

A force is exerted, the object moves as a result of the force, and the object moves in the direction of the force

Why is work done when a box is lifted vertically from the floor?

An upward force is exerted, the box moves upward as a result of the force, and the box moves in the direction of the force (upward)

Why is NO work done when a boy carries his suitcase horizontally?

The hand exerts an upward force (equal in magnitude to gravity on the case), but the suitcase moves horizontally forward, not in the direction of the upward force

Why is NO work done when a boy pushes on a wall that doesn't move?

The boy exerts a force on the wall, but the wall does not move

What is the formula to calculate work?

Work = Force x distance (in the direction of the force), i.e. W = F x d

Symbol, physical quantity, and SI unit for W

Symbol: W, Quantity: Work, Unit: J (joule)

Symbol, physical quantity, and SI unit for F

Symbol: F, Quantity: Force, Unit: N (newton)

Symbol, physical quantity, and SI unit for d

Symbol: d, Quantity: Distance (in direction of force), Unit: m (metre)

How are work and energy related?

Work and energy are equivalent - work transfers energy, and energy causes work to be done; any form of energy is also measured in joules

If a force of 2 N moves an object a distance of 3 m in the direction of the force, how much work is done?

W = F x d = 2 x 3 = 6 J

What is the definition of a joule?

One joule of work is done on an object when a force of 1 N causes the object to move a distance of 1 m in the direction of the force (1 J = 1 N times 1 m)

How many joules are in a kilojoule?

1 kJ = 1 000 J

Worked Example: A spring balance pulls an object 2 m across a bench with a recorded force of 10 N. Calculate the work done.

W = F x d = 10 x 2 = 20 J

Worked Example: A motor car does 30 000 J of work to move a distance of 5 m. Calculate the force exerted by the engine.

F = W / d = 30 000 / 5 = 6 000 N

Worked Example: A girl's suitcase has a weight of 12 N and is lifted vertically onto a 60 cm high table. How much work is done?

60 cm divided by 100 = 0,6 m; W = F x d = 12 x 0,6 = 7,2 J

A boy of mass 40 kg runs up a flight of stairs (5 m incline, 4 m base, 3 m height). What is his weight (Fg)?

Fg = m x g = 40 x 9,8 = 392 N

In the stair-climbing example, which distance is used to calculate the work done against gravity, and why?

The vertical distance (3 m) is used, because for work to be done, the force (weight, acting downward) and the distance moved must be in the same direction

Worked Example: Boy on stairs - calculate the work done against gravity to reach the top.

W = F x d = 400 x 3 = 1 200 J

How do you calculate work done in a horizontal plane?

The force acting on the object must be given or calculated directly - you do NOT use the object's weight as the force

How do you calculate work done in a vertical plane?

The weight must be used as the force; if only the mass in kg is given, the weight must be calculated first (Fg = mg)

If an object is lifted at an angle, which distance must be used to calculate work done against gravity?

The vertical distance must be used, because it is in the same direction as the weight

What is the definition of Energy?

Energy is the ability to perform work

What is the Law of Conservation of Energy?

Energy can neither be created nor destroyed, it can only be transformed from one form to another

What is the unit of Energy?

The same as for Work: Joules (J)

All forms of energy fall into which two categories?

Kinetic energy and potential energy

What is the definition of Potential Energy?

Potential energy is the energy that is stored in an object due to its position relative to some zero position (e.g. gravitational potential energy from height above or below the earth)

What is the formula for Potential Energy, and what do the symbols mean?

PE = mgh, where PE = potential energy (J), m = mass (kg), g = gravitational field strength (Earth = 9,8 N/kg), h = height above zero level (m)

What is the definition of Kinetic Energy?

The kinetic energy of an object is the energy it has due to its motion

What is the formula for Kinetic Energy, and what do the symbols mean?

KE = half mv squared, where KE = kinetic energy (J), m = mass (kg), v = speed/velocity (m/s)

Worked Example: Calculate the potential energy of a 2 kg book on top of a bookcase 1 m above the floor.

PE = mgh = (2)(9,8)(1) = 19,6 J

Worked Example: Calculate the kinetic energy of an 850 kg car driving at 18 m/s.

KE = half mv squared = half(850)(18) squared = 137 700 J

Worked Example: A garage hoist lifts a 1000 kg truck 2 m in 15 seconds. What is the force needed to lift it against gravity?

F = mg = 1000 x 9,8 = 9 800 N

Worked Example (continued): What is the work done lifting the truck 2 m?

W = F x d = 9 800 x 2 = 19 600 J

Worked Example (continued): What is the power delivered to lift the truck?

P = W / t = 19 600 / 15 = 1 306,67 W

What is the formula for Power?

P = W / t, where P = power, W = work done (J), t = time (s)

Worked Example: A garage hoist lifts a 1000 kg truck 2 m in 15 seconds. What is the force needed to lift it against gravity?

F = mg = 1000 x 9,8 = 9 800 N

Worked Example (continued): What is the work done lifting the truck 2 m?

W = F x d = 9 800 x 2 = 19 600 J

Worked Example (continued): What is the power delivered to lift the truck?

P = W / t = 19 600 / 15 = 1 306,67 W