Download A Newton`s 2nd Law

A– LEVEL TOPIC REVIEW
unit M1
dynamics of a particle 1
If a numerical value of g is required, take g = 9.8 ms-2.
Give all non-exact answers correct to 3 significant figures unless otherwise specified.
1. A stone of mass 3 kg is projected along the surface of a frozen pond. It is given an initial
velocity of 4 ms-1 and comes to rest after travelling 40 m in a straight line.
Calculate the coefficient of friction between the stone and the surface.
(7 marks)
2. A particle P of mass 4 kg moves in a horizontal plane under the action of a constant force
(2i – 8j) N. 6 seconds after the force starts acting, the velocity of P is (3i + 7j) ms-1.
a) Find the velocity vector of P when the force starts acting.
(4 marks)
b) Find the time that has elapsed when the body is moving parallel to the vector i.
(3 marks)
3. A boy of mass 40 kg stands in a lift. Find the force exerted by the floor of the lift on the boy
when
a) the lift is moving upwards with constant speed,
(2 marks)
b) the lift is moving downwards with acceleration 1.4 ms-2.
(3 marks)
4. A small package P of mass 0.3 kg, which may be modelled as a
particle, is placed on the surface of a rough plane inclined at an angle θ
to the horizontal, where sin   53 , as shown. The coefficient of
friction between P and the plane is 14 . P is released from rest at a point
P
2m

2 m from the foot of the plane. Find
a) the acceleration of P down the plane,
b) the velocity with which P reaches the foot of the plane.
(6 marks)
(3 marks)
5. Two particles are connected by a light inextensible string which passes over a fixed smooth
pulley. The particles are released from rest with the string on either side of the pulley taut and
vertical. Find, in terms of g, the acceleration of the particles and the tension in the string if the
masses of the particles are
a) 0.1 kg and 0.4 kg,
(6 marks)
b) x kg and y kg, where x < y.
(7 marks)
6. A body A, of mass 1 kg, lies on a smooth horizontal table. A is connected
by a light inextensible string, passing over a fixed smooth pulley, to a
body B of mass 0.8 kg hanging freely with the string taut. B is released
from rest. Find
a) the initial acceleration of the two particles,
(5 marks)
b) the time taken for B to fall 20 cm, given that A is initially more than 20
cm from the pulley.
(4 marks)
A
B
A– LEVEL TOPIC REVIEW : ANSWERS
unit M1
dynamics of a particle 1