Arrestor beds are used to help moving trucks to come to a stop when their brakes fail - NSC Physical Sciences - Question 5 - 2022 - Paper 1

The net work done on the truck is negative because the frictional force acting against the truck's motion on the arrestor bed does work that opposes its initial kinetic energy, resulting in a decrease in the truck's speed.

To calculate the minimum length of the arrestor bed, we use the work-energy principle:

1. The initial kinetic energy (KE_initial) of the truck is given by: $KE_{initial} = \frac{1}{2} m v^2 = \frac{1}{2} (30000 \, kg) (33 \, m/s)^2 = 16,385,000 \, J$

2. The work done by the net force (W_net) while moving up the arrestor bed includes work done by friction and work done against gravity: $W_{net} = F_{friction} \cdot d + mgh$

3. Rearranging gives us the formula to find the minimum length (d) needed: $\text{Work done = change in kinetic energy} \, \Rightarrow W_{net} = KE_{initial}$

4. Substituting values: $-F_{friction} \cdot d - mgh = -KE_{initial}$

   • where F_friction = 31000 N and h = d sin(28°) Solve for d: $-31000d - (30000)(9.81)(d \sin(28°)) = -16385000$ $d = 96.64 \, m$

The ASCENDING arrestor bed will be able to stop the truck in a shorter distance. This is because the truck moving uphill experiences a greater effective friction force as it opposes both its motion and the component of gravitational force acting down the slope. In contrast, on a DESCENDING arrestor bed, the gravitational force aids the motion of the truck, which requires more distance to stop as the frictional force is less effective compared to the ascending case.