What is a Momentum and Impulse, Grade 11 physics

Definition: Momentum
Momentum is the tendency of an object to continue to move in its direction of travel. Momentum is calculated from the product of the mass and velocity of an object.
The momentum (symbol p) of an object of mass m moving at velocity v is:

p = m · v​

According to this equation, momentum is related to both the mass and velocity of an object. A small car travelling at the same velocity as a big truck will have a smaller momentum than the truck. The smaller the mass, the smaller the velocity.

A car travelling at 120 km·hr$^{−1}$ will have a bigger momentum than the same car travelling at 60 km·hr$^{−1}$. Momentum is also related to velocity; the smaller the velocity, the smaller the momentum.

Different objects can also have the same momentum, for example a car travelling slowly can have the same momentum as a motor cycle travelling relatively fast. We can easily demonstrate this.

Consider a car of mass 1 000 kg with a velocity of 8 m·s$^{−1}$ (about 30 km·hr$^{−1}$). The momentum of the car is therefore

p = m · v = (1000)(8) = 8000 kg · m · s$^{−1}$​

Even though the motor cycle is considerably lighter than the car, the fact that the motor cycle is travelling much faster than the car means that the momentum of both vehicles is the same.

From the calculations above, you are able to derive the unit for momentum as kg·m·s$^{−1}$.
Momentum is also vector quantity, because it is the product of a scalar (m) with a vector (v).
This means that whenever we calculate the momentum of an object, we need to include the direction of the momentum.

Vector Nature of Momentum

Worked Example: Calculating the Total Momentum of a System
Question: Two billiard balls roll towards each other. They each have a mass of
0,3 kg. Ball 1 is moving at v₁ = 1 m · s$^{−1}$ to the right, while ball 2 is moving at v₂ = 0,8 m · s$^{−1}$ to the left. Calculate the total momentum of the system.

Answer

Step 1 : Identify what information is given and what is asked for
The question explicitly gives

• the mass of each ball,
• the velocity of ball 1, v₁, and
• the velocity of ball 2, v₂, all in the correct units!

We are asked to calculate the total momentum of the system. In this example our system consists of two balls. To find the total momentum we must determine the momentum of each ball and add them.

p$_{total}$ = p₁ + p₂​

Since ball 1 is moving to the right, its momentum is in this direction, while the second ball’s momentum is directed towards the left.

Step 2 : Choose a frame of reference
Let us choose right as the positive direction, then obviously left is negative.
Step 3 : Calculate the momentum
The total momentum of the system is then the sum of the two momenta taking the
directions of the velocities into account. Ball 1 is travelling at 1 m·s$^{−1}$ to the right or +1 m·s$^{−1}$ . Ball 2 is travelling at 0,8 m·s$^{−1}$ to the left or -0,8 m·s$^{−1}$ . Thus,
p$_{total}$ = m₁v₁ + m₂v₂ = (0,3)(+1) + (0,3)(−0,8) = +0,06 kg · m · s$^{−1}$= 0,06 kg · m · s$^{−1}$ to the right
In the last step the direction was added in words. Since the result in the second last line is positive, the total momentum of the system is in the positive direction (i.e. to the right).

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