4.24 Calculating Acceleration from Force and Mass
Calculating Acceleration
This equation for acceleration can be used to calculate the acceleration of an object that is acted on by a net force. For
example, Xander and his scooter have a total mass of 50 kilograms. Assume that the net force acting on Xander and
the scooter is 25 Newtons. What is his acceleration? Substitute the relevant values into the equation for acceleration:
a=mF= 5025 kgN=^0 .kg^5 N
The Newton is the SI unit for force. It is defined as the force needed to cause a 1-kilogram mass to accelerate at 1
m/s^2. Therefore, force can also be expressed in the unit kg • m/s^2. This way of expressing force can be substituted
for Newtons in Xander’s acceleration so the answer is expressed in the SI unit for acceleration, which is m/s^2 :
a=^0 .kg^5 N=^0.^5 kg·m/s
2
kg =^0 .5 m/s2Q: Why are there no kilograms in the final answer to this problem?
A: The kilogram units in the numerator and denominator of the fraction cancel out. As a result, the answer is
expressed in the correct SI units for acceleration.
Calculating Force
It’s often easier to measure the mass and acceleration of an object than the net force acting on it. Mass can be
measured with a balance, and average acceleration can be calculated from velocity and time. However, net force
may be a combination of many unseen forces, such as gravity, friction with surfaces, and air resistance. Therefore, it
may be more useful to know how to calculate the net force acting on an object from its mass and acceleration. The
equation for acceleration above can be rewritten to solve for net force as:
Net Force = Mass×Acceleration, or
F = m×a
Look at Xander in theFigure4.47. He’s riding his scooter down a ramp. Assume that his acceleration is 0.8 m/s^2.
How much force does it take for him to accelerate at this rate? Substitute the relevant values into the equation for
force to find the answer:
F = m×a = 50 kg×0.8 m/s^2 = 40 kg • m/s^2 , or 40 N
FIGURE 4.47
Q: If Xander and his scooter actually had a mass of 40 kg instead of 50 kg, how much force would it take for him to