A 70 kg box is initially at rest at the bottom of a ROUGH plane inclined at an angle of 30° to the horizontal - NSC Physical Sciences - Question 5 - 2019 - Paper 1

The mechanical energy of the system will not be conserved due to the presence of friction, which is a non-conservative force. Energy is lost to heat through friction as the box moves up the incline.

The free-body diagram includes:

• Weight (W) acting downwards, equal to mg.
• Tension (T) acting parallel to the incline.
• Normal force (N) acting perpendicular to the incline.
• Frictional force (f) acting in the opposite direction to the movement.

The diagram should show the forces clearly with appropriate labels.

The work done by the frictional force can be calculated using the formula:

$W = F imes d imes ext{cos}(180°)$

Where:

• $F = 178.22 \, N$ (frictional force)
• $d = 4 \, m$ (distance moved)

Thus, $W = 178.22 imes 4 imes (-1) = -712.88 \, J$

The negative sign indicates that work is done against the direction of movement.

To find the speed after moving 4 m, we can apply the work-energy principle:

• The net work done on the box is equal to the change in kinetic energy:

$W_{net} = ext{KE}_{final} - ext{KE}_{initial}$

Since the box starts from rest: $ext{KE}_{initial} = 0$

Thus, W_{net} = rac{1}{2} mv^2

Given the net work done is from the applied force and friction: $W_{net} = (700 imes 4) - 712.88$ $ext{Solving for the speed, } v:$ After calculations, we find that: $v = 4.52 \, m/s$

The total work done by friction consists of two phases:

1. Work done against friction as the box moves up:
   • $W_{friction, up} = -712.88 \, J$ (calculated above)
2. Work done by friction as the box slides back down:
   • The box will lose the same amount of energy as it gains going up, but since it is moving down, it is still in the direction against friction:
   • $W_{friction, down} = 712.88 \, J$ (the same magnitude, opposite direction)

Total work done by friction during both motions is thus: $Total \, W_{friction} = W_{friction, up} + W_{friction, down} = -712.88 + 712.88 = 0$