Mechanics Year 1 (AS) Unit Test 8: Forces and Newton’s Laws
1 A particle P is acted upon by three forces F1, F2 and F3 given by F1 = (6i – 4j) N
F2 2i 9 j N F3 ai bj N,
and where a and b are constants. Given that P
is in equilibrium,
a find the value of a and the value of b. (2 marks)
F2 F1 F3
The force is now removed. The resultant of and is R.
b Find the magnitude of R. (3 marks)
c Find the angle, to 0.1°, that R makes with i. (2 marks)
2 A cyclist of mass 80 kg is travelling with speed 18 m s−1. The cyclist stops
peddling and comes to rest, without braking, due to resistance forces totalling 120
N.
a Find how long it takes the cyclist to stop. (4 marks)
b Find the distance the cyclist travels before stopping. (2 marks)
c Describe one limitation in this model. (1 mark)
3 A particle of mass 6 kg is initially at rest and is then acted upon by a force
R =
ai 10 j N
on a bearing of 300°.
a Find the exact value of a. (3 marks)
b Calculate the magnitude of R. (2 marks)
c Work out the magnitude of the acceleration of the particle. (2 marks)
d Find the time it takes for the particle to travel a distance of 640 m. (2 marks)
4 A car of mass 1200 kg pulls a trailer of mass 400 kg along a straight horizontal
road. The car and trailer are connected by a tow-rope modelled as a light
inextensible rod. The engine of the car provides a constant driving force of 3200
N. The horizontal resistances of the car and the trailer are proportional to their
respective masses. Given that the acceleration of the car and the trailer is 0.4 m s −2,
a find the resistance to motion on the trailer, (4 marks)
b find the tension in the tow-rope. (3 marks)
When the car and trailer are travelling at 25 m s −1 the tow-rope breaks. Assuming
that the resistances to motion remain unchanged,
c find the distance the trailer travels before coming to a stop, (4 marks)
d state how you have used the modelling assumption that the tow-rope is
inextensible. (1 mark)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
Mechanics Year 1 (AS) Unit Test 8: Forces and Newton’s Laws
5 A box A of mass 0.8 kg rests on a rough horizontal table and is attached to one end
of a light inextensible string. The string passes over a smooth pulley fixed at the
edge of the table. The other end of the string is attached to a sphere B of mass 1.2
kg, which hangs freely below the pulley. The magnitude of the frictional force
between A and the table is F N. The system is released from rest with the string
taut. After release, B descends a distance of 0.9 m in 0.8 s. Modelling A and B as
particles, calculate
a the acceleration of B, (2 marks)
b the tension in the string, (3 marks)
c the value of F. (3 marks)
Sphere B is 0.9 m above the ground when the system is released. Given that it
does not reach the pulley and the frictional force remains constant throughout,
d find the total distance travelled by A. (7 marks)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2
