More practice questions

4. Q4. A truck of mass 2000 kg moving at 72 km/h is brought to rest in 5 s by its brakes. Find the net horizontal retarding force, assuming uniform deceleration along a straight level road.

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   u = 72 km/h = 20 m s⁻¹ and v = 0, so a = (0 − 20)/5 = −4 m s⁻². Then F = ma = 2000 × (−4) = −8000 N. The braking force is 8000 N (8 kN), opposite to the motion.

5. Q5. The only unbalanced forces on a body of mass 10 kg are 6 N and 8 N at right angles. Find the magnitude and direction of its acceleration.

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   $F_{\text{net}} = \sqrt{6^{2} + 8^{2}} = 10\ \text{N}$⁠, so a = 10/10 = 1 m s⁻². It points along the resultant, at θ = tan⁻¹(8/6) ≈ 53° to the 6 N force.

6. Q6. A bullet of mass 20 g is accelerated uniformly from rest along a 0.8 m gun barrel and leaves it at 400 m s⁻¹. Find the average force on the bullet.

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   From v² = u² + 2as:

   $$\begin{aligned}a &= \frac{400^2}{2\times0.8} \\ &= 1.0\times10^5\ \text{m s}^{-2}\end{aligned}$$

   . Then F = ma = 0.02 × 10⁵ = 2000 N.

7. Q7. A rope can withstand a maximum tension of 600 N. What is the largest upward acceleration with which it can lift a 50 kg load? Take g = 9.8 m s⁻².

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   T − mg = ma, so

   $$\begin{aligned}a &= \frac{T-mg}{m} \\ &= \frac{600-490}{50} \\ &= 2.2\ \text{m s}^{-2}\end{aligned}$$

   .

8. Q8. Sand falls vertically onto a horizontal conveyor belt at 2 kg s⁻¹. The belt moves at a constant 3 m s⁻¹. What additional horizontal driving force is needed to bring the arriving sand to this speed, neglecting other resistance?

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   The sand arrives with zero horizontal velocity and must be brought up to the belt’s speed. With v constant,

   $$\begin{aligned}F &= v\frac{dm}{dt} \\ &= 3\times2 = 6\ \text{N}\end{aligned}$$

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