Kinetic Energy Work Theorem
What is the equation for kinetic energy?
1/2 mv2
State the law of conservation of mechanical energy.
The total amount of mechanical energy, in a closed system in the absence of dissipative forces (e.g. friction, air resistance), remains constant.
Define work in terms of physics.
Work is the energy transferred to or from an object via the application of force along a displacement.
What is the SI unit for Energy?
Joules
Define power.
Power is rate of doing work, it is the work done in unit time.
Define the work-energy theorem.
The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.
What is Mechanical Energy?
Mechanical Energy consists of two types of energy - the kinetic energy (energy of motion) and the potential energy (stored energy of position), GPE and EPE.
Calculate the work done by a force of 15 N over a distance of 8 m.
120 J
Name the two main types of mechanical energy and briefly explain how they are related.
Kinetic energy is the energy of motion, while potential energy is stored energy related to an object's position.
A motor does 5000 joules of work in 10 seconds. Calculate the power of the motor.
Work / Time; Power = 5000 J / 10 s = 500 Watts
A cat knocks a 0.01kg toy mouse across the floor with 3N of force. If the cat did 12J of work, how far did the mouse travel?
4 m
The relationship between work, force, and distance is W=F∗s
We are given the force on the toy and the work done. Using these values, we can find the distance. Note that the mass is not relevant for this question.
12J=3N∗s
12J * 3N = s
4m= s
A ball with mass of 2kg is dropped from the top of a building this is 30m high. What is the approximate velocity of the ball when it is 10m above the ground?
20 ms-1
Use conservation of energy. The gravitational potential energy lost as the ball drops from 30m to 10m equals the kinetic energy gained.
What is the work done on a 45kg box that is being pushed with a 100N force for 5m?
500 J
Calculate the gravitational potential energy of a 10 kg object at a height of 5 m.
490 Joules
Define efficiency in the context of energy transformations
Efficiency is the ratio of useful output energy to the input energy, expressed as a percentage.
A bodybuilder is in the midst of a an intense training session. He is currently bench pressing a bar with a mass of 250kg. If he does six reps of this mass and his arms are 0.75m long, how much work has been done on the bar between the time the bar was removed from its rack and placed back on the rack?
0J
Explain how the law of conservation of energy applies to a roller coaster ride.
As a roller coaster moves, its potential energy is converted to kinetic energy and vice versa. The total mechanical energy remains constant in the absence of external forces like friction.
How does the angle between the force applied and the direction of motion affect the work done?
Work done is maximized when the force is applied in the direction of motion and decreases as the angle deviates from this direction.
A pear has a GPE of 14J and a mass of 275g. Calculate it’s height in m giving your answer to 2 decimal places.
5.19 m
If a machine takes in 1000 joules of energy and produces only 750 joules of useful work, what is the efficiency of the machine?
Efficiency = (Useful Energy Output / Total Energy Input) × 100; Efficiency = (750 J / 1000 J) × 100 = 75%
How does the work-kinetic energy theorem help explain the braking distance of a car?
The work done by friction in bringing the car to a stop is equal to the initial kinetic energy of the moving car.
A pendulum with a mass of 405 kg reaches a maximum height of 2.4m. What is its velocity at the bottom most point in its path?
6.9 ms-1
First solve for the potential energy of the pendulum at the height of 2.4m.
PE = mgh
PE = (405kg)(10m/s2)(2.4m) = 9720J
This must be equal to the maximum kinetic energy of the object.
KE = ½mv2
9720J = ½mv2
Plug in the mass of the object (405 kg) and solve for v.
9720J = ½(405kg)v2
v = 6.9m/s
What are the conditions for work done to be zero?
It can be summarised that no work is produced if:
Dana pulls a spring with a spring constant k = 300 Nm-1 stretching it from its rest length of 0.40 m to 0.50 m.
What is the elastic potential energy stored in the spring?
1.5 Joules
A certain large wind turbine is able to transform 1,500,000J of mechanical energy into 1,000,000J of electrical energy every second. Determine how much thermal energy does this turbine 'waste' each second and the efficiency of this turbine.
500,000 J wasted each second and ~67%