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P5 W) Momentum – Part 1
P5 W) Momentum – Part 1
All moving objects have momentum. All stationary objects have zero momentum. The momentum of a moving object depends on both the mass and the velocity of the object. Momentum is a vector quantity because it has magnitude (size) and direction. Momentum can be calculated using the formula:
In the above formula, p is momentum measured in kilogram metres per second (kg m/s), m is mass measured in kilograms (kg) and v is velocity measured in metres per second (m/s).
If we have two objects with different masses that have the same velocity, the object that has the greater mass will have the greater momentum. For example, if a car and a lorry both have a velocity of 20 m/s, the momentum of the lorry would be greater than the momentum of the car because the lorry has a greater mass.
If we have two objects with the same mass travelling at different velocities, the object with the greater velocity will have the greater momentum. For example, if we have two identical cars and one has a velocity of 10 m/s and the other has a velocity of 25 m/s, the car that has a velocity of 25 m/s would have the greater momentum as it has a higher velocity (25 m/s compared with 10 m/s).
Let’s now have a few calculation questions.
If we have two objects with different masses that have the same velocity, the object that has the greater mass will have the greater momentum. For example, if a car and a lorry both have a velocity of 20 m/s, the momentum of the lorry would be greater than the momentum of the car because the lorry has a greater mass.
If we have two objects with the same mass travelling at different velocities, the object with the greater velocity will have the greater momentum. For example, if we have two identical cars and one has a velocity of 10 m/s and the other has a velocity of 25 m/s, the car that has a velocity of 25 m/s would have the greater momentum as it has a higher velocity (25 m/s compared with 10 m/s).
Let’s now have a few calculation questions.
Example 1
A car has a mass of 2,900 kg and a velocity of 30 m/s. Find the momentum of the car.
We work out momentum by multiplying the mass of the car by the velocity of the car. The equation is shown below.
A car has a mass of 2,900 kg and a velocity of 30 m/s. Find the momentum of the car.
We work out momentum by multiplying the mass of the car by the velocity of the car. The equation is shown below.
We are told in the question that the mass of the car is 2,900 kg and the velocity of the car is 30 m/s. These values are in the correct units, so we can sub them into the equation.
The car has a momentum of 87,000 kg m/s.
Example 2
A roller skater has a velocity of 3 m/s and a momentum of 135 kg m/s. Find the mass of the roller skater?
We find the calculation that we undertake to find the mass of the roller skater by covering up mass (m) in the momentum formula triangle. When we cover up mass in the formula triangle, we can see that we can find the mass by dividing the momentum by the velocity.
A roller skater has a velocity of 3 m/s and a momentum of 135 kg m/s. Find the mass of the roller skater?
We find the calculation that we undertake to find the mass of the roller skater by covering up mass (m) in the momentum formula triangle. When we cover up mass in the formula triangle, we can see that we can find the mass by dividing the momentum by the velocity.
The question tells us that the momentum of the roller skater is 135 kg m/s and the velocity of the roller skater is 3 m/s. Both of these values are in the correct units, so we can sub them into the calculation.
Therefore, the roller skater has a mass of 45 kg.
Example 3
The momentum of a 40-gram bullet is 22 kg m/s. Find the velocity of the bullet.
We find the calculation that we undertake to find the velocity of the bullet by covering up velocity (v) in the momentum formula triangle. When we cover up velocity in the formula triangle, we can see that we can find the velocity by dividing the momentum by the mass.
The momentum of a 40-gram bullet is 22 kg m/s. Find the velocity of the bullet.
We find the calculation that we undertake to find the velocity of the bullet by covering up velocity (v) in the momentum formula triangle. When we cover up velocity in the formula triangle, we can see that we can find the velocity by dividing the momentum by the mass.
Momentum in the above calculation should be in kg m/s, and we are told in the question that the momentum of the bullet is 22 kg m/s. The mass in the above calculation should be in kilograms. The question tells us that the mass of the bullet is 40 grams, so we need to convert the 40 grams from grams to kilograms. There are 1,000 grams in 1 kilogram, so we convert 40 grams to kilograms by dividing by 1,000; the mass is 0.04 kg (40 ÷ 1,000 = 0.04). We now have all of the values in the correct units; the momentum is 22 kg m/s, and the mass is 0.04 kg.
The velocity of the bullet is 550 m/s.