Newton’s Second Law
Unbalanced forces
When the forces acting on an object do not balance, the The single force that could replace all the forces acting on an object, found by adding these together. If all the forces are balanced, the resultant force is zero. will cause the object to The rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. in the direction of the resultant force.
In other words, a resultant force on a body will cause it to change its The speed of an object in a particular direction.. This simply means that unbalanced forces will cause:
- acceleration
- deceleration
- change in direction
The relationship between the resultant force, the mass of the object and the object’s acceleration is:
\({\text{resultant force (N)}}={\text{mass (kg)}}\times{\text{acceleration (m/s}^{2}}{\text{)}}\)
\(\text{F}=\text{m}\times\text{a}\)
You will have to be able to state this equation in the examination.
Question
A car weighs 1,000 kg. The resultant force is 5,000 N. Use the Fma triangle to find the acceleration of the car.
Acceleration = resultant force ÷ mass
a = 5,000 N ÷ 1,000 kg = 5 m/s2
Resultant force and calculating acceleration
To calculate the acceleration, you must find the resultant force so that you can divide it with the car's mass.
The resultant force = 4,000 N - 1,000 N = 3,000 N
\(\text{acceleration}=\frac{\text{resultant force}}{\text{mass}}\)
= 3,000 N ÷ 1,000 kg
= 3 m/s2
The first car accelerates because the car is moving in the same direction as the resultant force. Now look at the second car.
Resultant force = -7,000 N
\(\text{acceleration}=\frac{\text{resultant force}}{\text{mass}}\)
= -7,000 N ÷ 1,000 kg
= -7 m/s2
The second car Slowing down or negative acceleration, eg the car slowed down with a deceleration of 2 ms⁻².. It is moving in the opposite direction to the resultant force.
Acceleration and mass are A relationship between two variables where as one variable increases, the other variable decreases, eg as the volume doubled, the pressure decreased by half.. This means that if the mass of the vehicle doubles, the acceleration halves if the resultant force doesn’t change.
Resultant force and acceleration are Relationship between two variables where one variable is equal to a constant multiplying the other variable. Variables are plotted as a straight line though the origin.. If the resultant force doubles, the acceleration of the vehicle also doubles if the mass of the vehicle is the same.
Question
A car has a mass of 1,200 kg, and an engine that can deliver a force of 6,000 N. Find the acceleration of the car.
a = F ÷ m
= 6,000 N ÷ 1,200 kg
= 5 m/s2
Question
Find the force developed by a speed boat engine, if the boat has a mass of 300 kg and can accelerate at a rate of 1.5 m/s2.
F = m × a
= 300 kg × 1.5 m/s2
= 450 N
Question
In a theme park, one of the rides has a motor that can deliver a force of 3,600 N to an empty passenger car, causing it to accelerate at 4.5 m/s2.
Find the mass of the car.
m = F ÷ a
= 3,600 N ÷ 4.5 m/s2
= 800 kg
