How to Calculate Force
Force equals mass times acceleration. The formula is the easy part; the marks are in noticing that F means the net force, and in getting the acceleration when the question hands you a velocity change instead.
The formula
F = ma, where F is the net force in newtons, m is the mass in kilograms, and a is the acceleration in metres per second squared. One newton is one kilogram metre per second squared, which is why the units only work if the mass is in kilograms.
Net force, not applied force
- Add up every force acting, with direction taken into account.
- Forces in opposite directions subtract, so a 50 N push against 20 N of friction is a 30 N net force.
- If the net force is zero the object does not accelerate, though it may still be moving.
Getting acceleration first
Many questions give a velocity change rather than an acceleration. Use a = change in velocity divided by time, then substitute into F = ma. Doing this in two clearly labelled steps is what keeps the units straight.
Worked examples
Example 1
Question
A 15 kg box accelerates at 4 m/s squared. What net force acts on it?
Answer
60 N
Steps
- 1Identify the knowns: m = 15 kg, a = 4 m/s squared.
- 2Apply F = ma.
- 3Substitute with units: F = 15 kg x 4 m/s squared.
- 4F = 60 kg m/s squared, which is 60 N.
Example 2
Question
A 0.145 kg baseball is stopped from 40 m/s in 0.005 s. Find the average force.
Answer
1160 N
Steps
- 1Acceleration first: a = change in velocity / time = 40 / 0.005.
- 2That gives a = 8000 m/s squared, a deceleration.
- 3Now apply F = ma: F = 0.145 x 8000.
- 4F = 1160 N, directed opposite to the motion.
- 5Sense check: a very short stopping time produces a very large force, which is why catching gloves are padded.
The size of this answer is the physics. Extending the stopping time is the only way to reduce the force, and that is the entire principle behind crumple zones and airbags.
Example 3
Question
A 6 kg crate is pushed with 50 N while friction opposes it with 20 N. Find its acceleration.
Answer
5 m/s squared
Steps
- 1Find the net force first: 50 N forward minus 20 N backward.
- 2Net force = 30 N in the direction of the push.
- 3Rearrange F = ma to a = F / m.
- 4a = 30 / 6 = 5 m/s squared.
Common mistakes
Using the applied force in F = ma when friction is also acting.
F is the net force. Combine all the forces with their directions before substituting.
Leaving mass in grams.
Convert to kilograms first. A mass in grams makes the answer 1000 times too large.
Confusing mass and weight.
Mass is in kilograms and does not change. Weight is a force in newtons, equal to mass times g.
Assuming zero net force means the object is stationary.
It means constant velocity, which includes moving steadily in a straight line.
Practice it
Work these out first, then open the answer. Stuck halfway? Select the problem and ask Solvecoon for the step you are missing.
1. A 25 kg object accelerates at 2 m/s squared. Find the net force.
Show answer
50 N, from F = 25 x 2.
2. A 90 N net force acts on a 30 kg mass. Find the acceleration.
Show answer
3 m/s squared, from a = F / m.
3. What is the weight of a 70 kg person on Earth, taking g as 9.8 m/s squared?
Show answer
686 N. Weight is mass times g, and it is a force, so the answer is in newtons.
Questions people ask
- What units should force be in?
- Newtons, provided mass is in kilograms and acceleration in metres per second squared. Mixed units are the most common source of a wrong answer here.
- How do I find force from a velocity change?
- Two steps. Divide the velocity change by the time to get acceleration, then multiply by mass.
- Is weight the same as mass?
- No. Mass is the amount of matter in kilograms; weight is the gravitational force on it in newtons. Your mass is the same on the Moon, your weight is not.
- What does a negative force mean?
- It acts in the opposite direction to the one you defined as positive. Declaring your positive direction before you start prevents most sign confusion.
Keep reading
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