Science: Work, Energy, and Power
Calculating force, motion, energy changes, and power
Science: Work, Energy, and Power
Calculating force, motion, energy changes, and power
Physics - Grade 9-12
- 1
A student pushes a box with a force of 25 N across a floor for 4 m in the same direction as the motion. How much work is done on the box?
Use the formula W = Fd when force and motion are in the same direction.
The work done on the box is 100 J. Work equals force times distance when the force is in the same direction as the motion, so W = 25 N x 4 m = 100 J. - 2
A waiter carries a tray horizontally across a room at constant height. The upward force from the waiter's hand is 60 N, and the tray moves 8 m horizontally. How much work does the upward force do on the tray?
Think about the angle between the force and the displacement.
The upward force does 0 J of work on the tray. Work depends on the component of force in the direction of motion, and here the force is vertical while the motion is horizontal. - 3
A 3 kg cart moves at 6 m/s. What is its kinetic energy?
The cart has 54 J of kinetic energy. Using KE = 1/2 mv^2, we get KE = 1/2 x 3 kg x (6 m/s)^2 = 54 J. - 4
A 2 kg book is lifted onto a shelf 1.5 m above the floor. What is the increase in gravitational potential energy of the book? Use g = 9.8 m/s^2.
Use the gravitational potential energy formula mgh.
The increase in gravitational potential energy is 29.4 J. Using GPE = mgh, we get 2 kg x 9.8 m/s^2 x 1.5 m = 29.4 J. - 5
A machine does 600 J of work in 12 s. What is its power output?
The power output is 50 W. Power is the rate of doing work, so P = W/t = 600 J / 12 s = 50 W. - 6
A 1200 W microwave runs for 30 s. How much energy does it use during that time?
Rearrange the power formula to solve for energy.
The microwave uses 36,000 J of energy. Since power equals energy divided by time, energy equals power times time, so E = 1200 W x 30 s = 36,000 J. - 7
A roller coaster car has 20,000 J of gravitational potential energy at the top of a hill. Neglecting friction, what will its kinetic energy be at the bottom if all of that potential energy is converted?
Its kinetic energy at the bottom will be 20,000 J. By conservation of energy, the lost gravitational potential energy becomes kinetic energy when friction is neglected. - 8
A 0.5 kg ball is dropped from a height of 10 m. Ignore air resistance. What is its speed just before it hits the ground? Use g = 9.8 m/s^2.
Set gravitational potential energy equal to kinetic energy.
The ball's speed is about 14 m/s just before impact. Using conservation of energy, mgh = 1/2 mv^2, so v = square root of 2gh = square root of 2 x 9.8 x 10, which is about 14 m/s. - 9
A crane lifts a 200 N load straight up by 5 m. How much work does the crane do on the load?
The crane does 1000 J of work on the load. Since the force and displacement are in the same direction, W = Fd = 200 N x 5 m = 1000 J. - 10
A 4 kg object speeds up from 2 m/s to 8 m/s. Find the change in kinetic energy.
Find the initial and final kinetic energies, then subtract.
The change in kinetic energy is 120 J. The initial kinetic energy is 1/2 x 4 x 2^2 = 8 J, and the final kinetic energy is 1/2 x 4 x 8^2 = 128 J, so the increase is 128 J - 8 J = 120 J. - 11
A student climbs a flight of stairs and gains 1800 J of gravitational potential energy in 15 s. What is the student's average power output?
The student's average power output is 120 W. Power equals energy transferred divided by time, so P = 1800 J / 15 s = 120 W. - 12
A car engine transfers 90,000 J of energy in 3 s. What is the engine's power in watts and kilowatts?
First calculate power in watts, then convert to kilowatts.
The engine's power is 30,000 W, which is 30 kW. Using P = E/t, we get 90,000 J / 3 s = 30,000 W, and dividing by 1000 gives 30 kW.