Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
A van with mass $4500\,\text{kg}$ is pulling a trailer with mass $750\,\text{kg}$ along a straight hill that slopes at angle $\theta$ to the horizontal, where $\sin \theta = 0.05$. The van and trailer are joined by a light rigid tow-bar parallel to the road. Constant resistive forces act on the van and the trailer, with $2500\,\text{N}$ on the van and $300\,\text{N}$ on the trailer.
(a)[4]
Given that the tow-bar tension is $450\,\text{N}$, determine the trailer’s acceleration and the van engine’s driving force.
(b(i))[5]
In a different situation, the van and trailer travel up a straight hill inclined at angle $\alpha$ to the horizontal, where $\sin \alpha = 0.09$. The van’s engine now provides a driving force of $9100\,\text{N}$, and the van’s speed at the foot of the hill is $20\,\text{m s}^{-1}$. The resistive forces are the same as before. Find the van’s acceleration and the tension in the tow-bar.
(b(ii))[2]
Determine the van’s speed after it has moved a distance of $375\,\text{m}$ up the hill.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law for the van, trailer, or the whole system” …