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1. A box of weight 100 N rests in equilibrium on a plane inclined at an angle α to the horizontal. It is given that sin α = 0.28 and cos α = 0.96. A force of magnitude P N acts on the box parallel to the plane in the upwards direction (see diagram). The coefficient of friction between the box and the plane is 0.25.

(i) Find the magnitude of the normal force acting on the box. = 96N
(ii) Given that the equilibrium is limiting, show that the magnitude of the frictional force acting on the box is 24 N.
=96*0.25 = 24N
(iii) Find the value of P for which the box is on the point of slipping:
(a) down the plane.

The mark scheme states the answer is P=4, from P = 100×0.28 – 24.Why is the answer less than 24N, which is the frictional force acting on the box to stop it from slipping?
2. Below
3. (Original post by Chelsea12345)
A box of weight 100 N rests in equilibrium on a plane inclined at an angle α to the horizontal. It is given that sin α = 0.28 and cos α = 0.96. A force of magnitude P N acts on the box parallel to the plane in the upwards direction (see diagram). The coefficient of friction between the box and the plane is 0.25.

(i) Find the magnitude of the normal force acting on the box. = 96N
(ii) Given that the equilibrium is limiting, show that the magnitude of the frictional force acting on the box is 24 N.
=96*0.25 = 24N
(iii) Find the value of P for which the box is on the point of slipping:
(a) down the plane.

The mark scheme states the answer is P=4, from P = 100×0.28 – 24.Why is the answer less than 24N, which is the frictional force acting on the box to stop it from slipping?
The frictional force is there to stop it from sliding down, which is 24N.

The weight, which is 100x0.28 is acting opposite to the frictional force, so friction is trying to keep it from falling, so it acts in the same direction as P, so

P + friction = 100 x 0.28
P = 100 x 0.28 - friction
P = 28 - 24
P = 4

Because the frictional force is acting opposite to which ever way the box is moving, if it’s moving down, so friction moves up, with P

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