← Momentum and impulse

Find the mass from the momentum

The third direction through the same equation: an object carries momentum 90 kg·m/s at 15 m/s, and its mass is the question. One more rearrangement completes the set.

Start from p = mv.

Make m the subject: divide both sides by v. That gives m = p/v.

Step 1: the values, unknown markedquantityvaluep90 kg·m/sv15 m/sm?
Step 1: write down the values, and mark the unknown.
Steps 2 and 3: rearrange, then substitutesteplineequationp = mvmake m the subjectm = p/vsubstitutem = 90 / 15 = 6.0resultm = 6.0 kg
Steps 2 and 3: make m the subject, then m = 90 / 15 = 6.0 kg.

With p in kg·m/s and v in m/s, the mass comes out in kilograms.

After this lesson you own all three directions through p = mv; from here, the work is reading which quantity a question wants.

Given the momentum and the velocity, make m the subject, m = p/v, then substitute and calculate. The mass comes out in kilograms.

An object carries momentum 90 kg·m/s at a velocity of 15 m/s. Calculate its mass.

Write down the values:

p = 90 kg·m/s, v = 15 m/s, m = ?

Write down the equation:

m = p/v

Substitute in the values, and calculate:

m = 90 / 15 = 6.0

The object's mass is 6.0 kg.

A ball carries momentum 5.4 kg·m/s at 4.5 m/s. Calculate its mass.

Write down the values:

p = 5.4 kg·m/s, v = 4.5 m/s, m = ?

Write down the equation:

m = p/v

Substitute in the values, and calculate:

m = 5.4 / 4.5 = 1.2

The ball's mass is 1.2 kg.

Quick-fire drill

A wagon carries momentum 44 kg·m/s at 4.0 m/s. Enter its mass in kg.

A cart carries momentum 150 kg·m/s at 2.5 m/s. Enter its mass in kg.

A ball carries momentum 10.5 kg·m/s at 3.5 m/s. Enter its mass in kg.

A truck carries momentum 2000 kg·m/s at 25 m/s. Enter its mass in kg.

A toy drone carries momentum 4.2 kg·m/s at 6.0 m/s. Enter its mass in kg.

A rowboat drifts at 1.5 m/s carrying momentum 270 kg·m/s. Enter the rowboat's mass in kg.

Your turn

A sled carries momentum 58.5 kg·m/s at 4.5 m/s. Enter its mass in kg.

A motorboat carries momentum 352 kg·m/s at 2.2 m/s. Enter its mass in kg.

A shopping cart rolls at 2.4 m/s carrying momentum 42 kg·m/s. Enter the cart's mass in kg.