← Newton's second and third laws

Solve for the mass

Here is the third direction through the same equation. A 6.0 N net force gives a drone an acceleration of 1.5 m/s². What is the drone's mass?

One more rearrangement completes the set.

Start from a = F_net/m.

Multiply both sides by m: m × a = F_net.

Divide both sides by a: m = F_net/a.

StepLinestarta = F_net/mmultiply both sides by mm × a = F_netdivide both sides by am = F_net/a
Two steps, each shown: m = F_net/a.

With F_net in newtons and a in m/s², the mass comes out in kilograms.

QuantityValueF_net6.0 Na1.5 m/s²m?
The same four solving steps as always, with m as the unknown.

You now own all three directions through a = F_net/m. From here, the work is reading which quantity a question wants.

To find a mass, make m the subject: m = F_net/a. With F_net in newtons and a in m/s², the answer comes out in kilograms.

A 6.0 N net force gives a drone an acceleration of 1.5 m/s². Calculate the drone's mass.

Write down the values in the question:

F_net = 6.0 N

a = 1.5 m/s²

m = ?

Write down the equation:

a = F_net/m

Make m the subject:

m = F_net/a

Substitute in the values:

m = 6.0 ÷ 1.5

Simplify:

m = 4.0 kg

The drone's mass is 4.0 kg.

The net force on a loaded canoe is 150 N, and it accelerates at 2.0 m/s². Calculate its total mass.

Write down the values in the question:

F_net = 150 N

a = 2.0 m/s²

m = ?

Write down the equation:

a = F_net/m

Make m the subject:

m = F_net/a

Substitute in the values:

m = 150 ÷ 2.0

Simplify:

m = 75 kg

The loaded canoe's total mass is 75 kg.

Quick-fire drill

A 28 N net force gives a stroller an acceleration of 4.0 m/s². Enter the stroller's mass in kg.

A 90 N net force accelerates a sled at 6.0 m/s². Enter the sled's mass in kg.

A 5.5 N net force gives a toy truck an acceleration of 2.2 m/s². Enter the toy truck's mass in kg.

A 640 N net force accelerates a boat at 0.80 m/s². Enter the boat's mass in kg.

A 42 N net force gives a wagon an acceleration of 3.5 m/s². Enter the wagon's mass in kg.

A tow rope accelerates a small trailer at 2.6 m/s² when the net force on the trailer is 1300 N. Enter the trailer's mass in kg.

Your turn

A 76 N net force gives a carry-on suitcase an acceleration of 9.5 m/s². Enter the suitcase's mass in kg.

The net force on a riding mower is 54 N while it accelerates at 1.2 m/s². Enter the mower's mass in kg.

At a trailhead, a packed utility cart is towed from rest and accelerates at 3.0 m/s² while the net force on it is 2100 N. Enter the cart's mass in kg.