Moderate -0.3 This is a straightforward energy conservation problem requiring students to equate loss in gravitational PE plus initial KE to final KE plus work done against resistance. It's a standard M2 application with clear given values and a single-step energy equation to solve, making it slightly easier than average but still requiring proper setup of the work-energy principle.
1 A boy on a sledge slides down a straight track of length 180 m which descends a vertical distance of 40 m . The combined mass of the boy and the sledge is 75 kg . The initial speed is \(3 \mathrm {~ms} ^ { - 1 }\) and the final speed is \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The magnitude, \(R \mathrm {~N}\), of the resistance to motion is constant. By considering the change in energy, calculate \(R\).
1 A boy on a sledge slides down a straight track of length 180 m which descends a vertical distance of 40 m . The combined mass of the boy and the sledge is 75 kg . The initial speed is $3 \mathrm {~ms} ^ { - 1 }$ and the final speed is $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The magnitude, $R \mathrm {~N}$, of the resistance to motion is constant. By considering the change in energy, calculate $R$.
\hfill \mbox{\textit{OCR M2 2009 Q1 [5]}}