Y12 Newton's Second Law

Newton’s Second Law of Motion
(Use g = 9.8 N kg^-1)

Worked example

Find the acceleration of a body of mass 10kg when it is subjected to a horizontal force of 100 N if it (a) can move along a smooth horizontal surface, (b) can move along a horizontal surface which produces a frictional force of 80N.
(a) F=ma      F force in N, mass in kg, a acceleration in ms^-2
Rearranging  a = F/m        a = 100 / 10  = 10 ms^-2

(b) The resultant force = 100 N – 80 N = 20 N

F=ma rearranging a = F/m
 a = 20 /10   a = = 2ms^-2  

1. A force of 100 N acts on a mass of 1 kg. What is the acceleration?
2. A mass of 10kg acquires a velocity of 20 m s from rest in 4 s. Calculate the force is required.
3. A rocket of mass 800 000 kg has motors giving a thrust of 9 800 000 N. Calculate the acceleration at lift off.
4. A force of 5 N acts on a stationary mass of 2kg which can move along a smooth horizontal surface. Calculate its velocity after 5 s?
5. A car of mass 600 kg travelling at 72km h^-1 is brought to rest in 54 m after the driver sees an obstruction ahead. If the distance travelled after the driver applies the brakes is 40m calculate the driver’s reaction time and the braking force.
6. A mass of 2kg projected along a flat surface with a velocity of 15ms^-1 comes to rest after travelling 30 m. Calculate the frictional force.
7. A Mini of mass 576 kg can accelerate from rest to 72 km h^-1 in 20 s. If the acceleration is assumed uniform calculate this acceleration and the tractive force in Newtons needed to produce it.
8. A Mini of mass 576 kg can be stopped (in neutral) in 72 m from 108 kmh^-1. Calculate (a) the deceleration, (b) the frictional force between the tyres and the road in Newtons.
9. The first-stage rocket motors of the Apollo spacecraft produce a thrust of 3.3 x 10⁷ N and the complete spacecraft has a mass of 2.7 x 10⁶ kg. Calculate (a) the resultant force accelerating the spacecraft, (b) the initial acceleration, (c) the time for it to rise through a distance equal to its own height as it ‘lifts off’ if its height is 111 m and the average acceleration during this time is 2.5 ms^-2
10. A boy of mass 50kg stands in a lift. What will he ‘weigh’ in Newtons if the lift accelerates at 0.50 ms^-2 (a) upwards, (b) downwards?