Force and acceleration
F=ma
When an object changes speed (accelerates or decelerates),its shape or direction of motion, a force is acting on it. The formula for force is given below.
F=mass(kg)
X acceleration(m/s/s)
The unit
of force is called the newton.
A 100 kg person standing on wooden floor boards exerts
a force of 1000 newtons on the floor.
Example. A 300g
cart reaches a speed of 50m/s in 20 seconds from a standing start. What
is the magnitude of the force acting on it?
Step 1 Change all units of mass into Kg . => 300g = 0.3Kg.
Step 2 Calculate the acceleration of the cart.
=> Acceleration = (final speed - initial speed)/time taken = (50
- 0)/20 =2.5m/s/s
Step 3 Calculate the force => F =ma = 0.3
X 2.5 = 0.75 newtons.
Exercises(F =ma)
We
can manipulate the formula (F =ma) to work out
the mass or the acceleration of the cart.
a
= f/m
or
m = f/a
Example. What is the acceleration
of a 2kg brick thrown with a force of 4 newtons?
Step 1 Make sure all measurements are in correct units. (In this case
they are)
Step 2 Calculate the acceleration using the formula a = f/m
=> a = 4/2 = 2m/s/s
Exercises(a =f/m)
Example. Jonathon has an engine
that can provide a force of 5.6 newtons. He wants to place the engine
on a cart so it accelerates at 3.5m/s/s. What should the combined mass
of the cart and engine be to achieve this acceleration?
Step 1 Make sure all measurements are in correct units. (In this case
they are)
Step 2 Calculate the mass of the vehicle using the formula m
= f/a
=> m = 5.6/3.5 = 1.6Kg
Exercises(m =f/a)