Work and energy

WME02Topic 2.33 questions

Work done, kinetic and potential energy, the work-energy principle and power.

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Question 15 marks
A car of mass $1200\,\text{kg}$ has an engine working at a constant rate of $24\,\text{kW}$ . The resistance to motion is constant and of magnitude $600\,\text{N}$ .

(a) Find the acceleration of the car when it is travelling along a level road at $15\,\text{m s}^{-1}$ .

(b) The car now drives up a straight road inclined at an angle $\theta$ to the horizontal, where $\sin\theta = \tfrac{1}{20}$ . Find the maximum speed of the car up this road.
Mark scheme
- (a) M1 Driving force $= \dfrac{24\,000}{15} = 1600\,\text{N}$ (1)
- M1 $F = ma$ : (1)
Question 26 marks
A particle of mass $3\,\text{kg}$ is projected up a line of greatest slope of a rough plane inclined at $30^\circ$ to the horizontal. Its initial speed is $8\,\text{m s}^{-1}$ and the coefficient of friction between the particle and the plane is .

1600 - 600 = 1200a

a = 0.833\,\text{m s}^{-2}

(1)

(b) M1 At maximum speed:

\dfrac{24\,000}{v} = 600 + 1200g \times \tfrac{1}{20}

(1)

v = 20.2\,\text{m s}^{-1}

(1)

−1

0.2

(a) Use the work–energy principle to find the distance the particle travels up the plane before coming to rest.

(b) The particle then slides back down. Find its speed when it returns to its starting point.

Mark scheme

(a) B1 $R = 3g\cos 30^\circ = 25.5\,\text{N}$ (1)
B1 $F = 0.2R = 5.09\,\text{N}$ (1)
M1 Work–energy: $\tfrac{1}{2}(3)(8^2) = 3g\sin 30^\circ \times d + 5.09d$ (1)
A1 $d = 4.85\,\text{m}$ (1)
(b) M1 $\tfrac{1}{2}(3)v^2 = 3g\sin 30^\circ \times 4.85 - 5.09 \times 4.85$ (1)
A1 $v = 5.57\,\text{m s}^{-1}$ (5.6) (1)

sin

0∘

5.09d

0∘

4.85−

5.09×

4.85