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Each of these problems is an example of Newton’s 2nd law.

Net force = mass * acceleration

The acceleration of an object is directly proportional to the net force. If the force is doubled, the acceleration will be doubled.

A 14.5 kg mass attached to a spring scale rests on a smooth, horizontal surface. The spring scale, attached to the front end of a boxcar, reads T = 31.7 N when the car is in motion. If the spring scale reads zero when the car is at rest, determine the acceleration of the car, when it is in motion as indicated above.

Answer in units of m/s2

In this problem, the net force is the tension.

T = m * a

The spring scale is used to measure force. When the car is at rest, force is 0, because the acceleration is 0.

31.7 = 14.5 * a

a = 31.7/14.5 ≈ 2.19 m/s^2

A force is applied to a 1.6 kg mass and produces 5.6 m/s2 acceleration. What acceleration would be produced by the same force applied to a 13.3 kg mass?

Answer in units of m/s2

F = 1.6 * 5.6 = 8.96 N

This is the force that causes the 13.3 kg object to accelerate.

8.96 = 13.3 * a

a = 8.96 ÷ 13.3

Suppose a cart is being moved by a certain net force. If the net force is increased by a factor of 4.7, by what factor does its acceleration change?

Net Force = m * a

F = Initial net force

Initial a = F/m

Increase = 4.7 * F

Final force = F + 4.7 * F = 5.7 * F

a = (5.7 * F) ÷ m

Final a = 5.7 * F/m

Increase = Final – Initial = 5.7 * F/m – F/m

Increase = 4.7 * F/m

The acceleration increased by the same factor as the force, because the acceleration is directly proportional to the force!

Suppose you have an object of mass m (in units of kg). If the total force on it is F (in units of newtons) then the object accelerates with an acceleration 'a' (in units m/s²).

F, m and a are related by the equation: F = ma, which you will need to learn.

The equation can be rearranged if required to give a = F/m and m = F/a.

E.g. A 20N force is applied to a 4kg mass; what is the mass's acceleration?

a = F/m = 20/4 = 5m/s²

That's all you need to know!

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Q1 A force of 31.7N is applied to a 14,5kg mass.

a = F/m = 31.7/14.5 = 2.19m/s²

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Q2 Start by finding the force which when applied to the 1.6 kg mass produces a 5.6 m/s² acceleration.

F = ma = 1.6 x 5.6 = 8.96N

Now find what acceleration this 8.96N force produces when applied to a mass of 13.3kg

a = F/m = 8.96/13.3 = 0.674 m/s²

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Q3 You have to understand proportionality for this, which is maths. So if you are not good at maths, this is tricky to explain.

Look at the equation a = F/m. 'm' is some fixed value. That means force and acceleration are proportional - if one changes by a certain factor the other must change by the same factor. E.g if force doubles, acceleration must double.

Using proportionality we can therefore say if F increases by a factor 4.7 (i.e. get 4.7 times bigger) then acceleration must also increase by a factor of 4.7.