P1 B) Kinetic Energy
When an object speeds up, energy is transferred to the object’s kinetic energy store. And, when an object slows down, energy is transferred away from the object’s kinetic energy store.
The kinetic energy of an object depends on its mass and speed. Kinetic energy has the following formula:
Where, EK is kinetic energy measured in joules (J), m is the mass measured in kilograms (kg) and v is the speed measured in metres per second (m/s).
We must be very careful when using this formula because it is not as straightforward as some of the other physics formulas. There are two key parts that we need to watch out for. The first one is remembering the ½ at the beginning of the formula. The second is remembering that we square the velocity of the object.
From the above formula, we can see that the kinetic energy store of an object depends on the mass and the speed of the object.
- If we have 2 objects with different masses that are travelling at the same speed, the object with the larger mass will have a greater amount of energy in its kinetic energy store.
- If we have 2 objects that have the same mass that are travelling at different speeds, the object that is travelling at a faster speed will have a greater amount of energy in its kinetic energy store.
Let’s now have a look at a few examples of using the kinetic energy formula.
An object has a mass of 4 kg and is travelling at a speed of 8 m/s. Find the amount of energy in the object’s kinetic energy store.
We find the kinetic energy (Ek) of the object by using the formula below.
m in the above formula is mass measured in kilograms, and the question tells us that the mass of the object is 4 kg. v in the above formula is speed measured in metres per second (m/s), and the question tells us that the speed is 8 m/s. Therefore, we find the kinetic energy (Ek) by subbing m in as 4 and v in as 8.
A car has a mass of 2,900 kg and is travelling at a speed of 35 m/s. Find the amount of energy in the car’s kinetic energy store.
Like the question before, we find the amount of energy in the car’s kinetic energy store (Ek) by using the formula below.
m in the above formula is mass measured in kilograms, and the question tells us that the mass of the car is 2,900 kg. v in the above formula is speed measured in metres per second (m/s), and the question tells us that the speed is 35 m/s. Therefore, we find the kinetic energy (Ek) by subbing m in as 2,900 and v in as 35.
We are now going to have a look at a more complex example whereby we are asked to find the speed of an object when we are given the amount of energy in the object’s kinetic energy store and the mass of the object. We answer questions like this by subbing all of the values that we are given into the formula for kinetic energy. We then solve to find the value of the unknown that we are looking for.
Question
An object has a mass of 24 kg. It is travelling at an unknown speed and has 432 joules in its kinetic energy store. Find the speed that the object is travelling at.
We can find the speed of the object by using the kinetic energy formula below.
The question is asking us to find the speed that the object is travelling at, which is v in the above formula. We are told in the question that the amount of energy in the object’s kinetic energy store is 432 joules and the mass of the object is 24 kg. We sub in EK as 432 and the mass as 24.
We now solve to find the value of v. The first step in solving is to multiply ½ by 24, which gives us 12. The equation becomes.
The next step is to get v2 by itself, which we do by dividing both sides of the equation by 12.
We want to find the value of v and not v2. Therefore, we square root both sides of the equation.
This tells us that the speed of the object is 6 m/s.