Momentum

Driving a car or driving a big truck - which is easier to change direction? With the same velocity, which is more difficult to stop? The mass and velocity of an object affect its motion. It is easier to change the direction of the car than the big truck since the car has lesser mass than the truck. Running at the same speed, stopping a truck is more difficult than stopping the car. This property of an object to continue motion along its direction is called momentum. When the object is in straight motion, the term often used is linear momentum.

Momentum is expressed mathematically as

$$p=mv$$

where $$p$$ is the momentum of the object in $$kg\cdot m/s$$, $$m$$ is the mass of the object in $$kg$$ and $$v$$ as the velocity in $$m/s$$.

Example 1.

A $$5.0-kg$$ object is moving at $$25 \;m/s$$. What is the object's momentum?

Given:

$$m=5.0 \;kg\\ v=25\;m/s$$

Solution:

$$p=mv\\ \;\;=(5.0\;kg)(25\;m/s)\\ \;\;=125\;kg\cdot m/s.$$

Example 2.

The momentum of a $$50\;kg$$ runner is $$650 \;kg\cdot m/s$$. Compute for the runner’s velocity.

Given:

$$m=50\;kg\\ p=650\;kg\cdot m/s$$

Solution:

$$v=\frac pm=\frac{650\;kg}{50\;kg}=13\;m/s$$.

Example 3.

Find the momentum of an adult cheetah with a mass of 68 kg if it covers a distance of $$1.92 \times 10^3 \;m$$ running in 1 minute?

Given:

$$m=68\;kg\\ d=1.92 \times 10^3\;m\\ t=1\;min=60\;s$$

Solution 1:

First solve for the speed of the cheetah.

$$v=\frac dt=\frac {1.92 \times 10^3\;m}{60\;s}=32\;m/s$$

Solution 2:

Compute for momentum using the velocity solved.

$$p=mv\\ \;\;=(68\;kg)(32\;m/s)\\ \;\;=2,176\;kg\cdot m/s$$

The momentum of the cheetah is $$2.176\times 10^3\;kg\cdot m/s$$.