OCR M2 2010 January — Question 4 10 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2010
SessionJanuary
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPower and driving force
TypeMaximum speed on incline vs horizontal
DifficultyStandard +0.3 This is a standard M2 mechanics question requiring straightforward application of F=ma, P=Fv, and resolving forces on an incline. All parts follow directly from standard formulas with no problem-solving insight needed, making it slightly easier than average for A-level.
Spec3.03d Newton's second law: 2D vectors3.03v Motion on rough surface: including inclined planes6.02k Power: rate of doing work6.02l Power and velocity: P = Fv

4 A car of mass 700 kg is moving along a horizontal road against a constant resistance to motion of 400 N . At an instant when the car is travelling at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) its acceleration is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  1. Find the driving force of the car at this instant.
  2. Find the power at this instant. The maximum steady speed of the car on a horizontal road is \(35 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  3. Find the maximum power of the car. The car now moves at maximum power against the same resistance up a slope of constant angle \(\theta ^ { \circ }\) to the horizontal. The maximum steady speed up the slope is \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  4. Find \(\theta\).

4 A car of mass 700 kg is moving along a horizontal road against a constant resistance to motion of 400 N . At an instant when the car is travelling at $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ its acceleration is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(i) Find the driving force of the car at this instant.\\
(ii) Find the power at this instant.

The maximum steady speed of the car on a horizontal road is $35 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(iii) Find the maximum power of the car.

The car now moves at maximum power against the same resistance up a slope of constant angle $\theta ^ { \circ }$ to the horizontal. The maximum steady speed up the slope is $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(iv) Find $\theta$.

\hfill \mbox{\textit{OCR M2 2010 Q4 [10]}}