Q1.
A car travelling at 72km/hr along a straight, level road is brought uniformly to a stop in a
distance of 40m. The car weight 8.80x103N. Find the breaking force.
Q2. A particle moves in a horizontal plane, in which the unit vectors î and ĵ are directed east and
north respectively. At time t seconds, its position vector, ȓ metres, is given by
ȓ = (2t3-t2+6)î+(8-4t3+t)ĵ
a) Find an expression for velocity at time t. (3m).
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b) (i) Find the velocity of the particle when t= . (2m)
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(ii) State the direction in which the particle is travelling at this time. (1m)
c) Find the acceleration of the particle when t=4. (3m)
d) The particle has a mass of 6kg. Find the magnitude of the resultant force on the
particle when t=4
Q3. The potential of a particle moving in the x y plane is given by Φ=2x2-5xy+3y2+6x-7y.
a) Prove that there will only be one and only one point of equilibrium.
b) Find the co-ordinate of this point.
Q4. A particle P is acted upon by 3 coplanar forces as indicated on the figure below. Find the
forces needed to prevent P from moving.
Q5. Prove that a particle which moves in a force field of potential
Φ=x2+4y2+ƶ2-4xy-4yz+2xƶ-4x+8y-4ƶ can remain in equilibrium at infinitely many points and
locate these points.
Q6. Find the angle of incline if coefficient of static friction is 0.9.
Q7. Find the work done by a child of mass 16kg whilst climbing to the top of a slide of vertical
height 9m.
Q8.A horizontal force P pulls a body mass 2.75 of a distance of 12m across a rough horizontal
surface, coefficient of friction 0.2. The body moves with a constant velocity and the only
resisting force is that due to friction. Find the work done against friction.
Q9. A rough surface is inclined at an angle cos-1(12/13) to the horizontal. A body of mass 140kg
lies on the surface and is pulled at a uniform speed a distance of 45m up the surface by a force
acting along the line of greatest slope. The coefficient of friction between the body and the
surface is (2/7). Find
a) The friction force acting
b) The work done against friction
c) The work done against gravity
Q10. A sledge is pulled across a smooth horizontal floor by a force of 50N inclined at 35 0 to the
horizontal. Find the work done by the force in moving the sledge a distance of 23m.
ASSIGNMENT TWO QUESTIONS
Q1. A golf ball is struck from a point 0 with velocity 24ms-1 at an angle of 400 to the horizontal.
The ball first hits the ground at a point P, which is at a height h metres above the level of 0.
The horizontal distance between 0 and P is 57m.
a) Show that the ball takes 3.10 sec (to 3S.F) to move from 0 to P. (3m)
b) Find the value of h. (3m)
c) (i) Find the speed with which the ball hits the ground at P. (5m)
(ii) Find the angle between the direction of motion and the horizontal as the ball hits the
ground at P. (2m)
Q2. A worker pulling a crate applies a force of 300 to the horizontal as shown below.
The crate has a mass of 40kg and the coefficient of friction between the surfaces is 0.65.
a) Calculate the force that must be applied to move the crate.
b) Calculate the force the worker requires to move the crate if the force is applied
horizontal i.e at 0o to the horizontal.
c) Compare your answers.
