More practice questions

4. Q4. Three blocks of masses 1 kg, 2 kg and 3 kg stand in a row on a smooth floor, touching. A horizontal force of 12 N pushes the 1 kg block. Find the acceleration and the contact force between each pair of blocks.

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   The whole row accelerates at 12/6, that is 2 m s^⁻². The force between the 1 kg and 2 kg blocks must accelerate the 2 kg and 3 kg blocks together: 5 × 2, that is 10 N. The force between the 2 kg and 3 kg blocks accelerates only the 3 kg block: 3 × 2, that is 6 N.

5. Q5. A rope lifts a 5 kg load with an upward acceleration of 2 m s^⁻². Find the tension in the rope. Take g = 9.8 m s⁻².

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   On the load, the tension acts up and the weight down: T − mg = ma. So

   $$\begin{aligned} T &= m(g + a) \\ &= 5(9.8 + 2) \\ &= 59\ \text{N} \end{aligned}$$

6. Q6. A 3 kg wooden block rests on a soft floor. A 20 kg iron cylinder is placed on it, and the floor yields so that the block and cylinder go down together with an acceleration of 0.2 m s^⁻². Find the force of the floor on the block. Take g = 9.8 m s⁻².

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   Take the block and cylinder together as the system (23 kg). The forces on it are its weight down and the floor’s normal force R up, and it accelerates down:

   $$\begin{aligned} mg - R &= ma \\ R &= m(g - a) \\ &= 23(9.8 - 0.2) \\ &= 220.8\ \text{N} \end{aligned}$$

   This is a little less than the weight, 225.4 N. Compare NCERT Example 4.12, which works the same idea with a 2 kg block and a 25 kg cylinder.

7. Q7. A 4 kg block rests on a table with μ_s = 0.3. It is tied by a string over a smooth pulley at the edge to a hanging block. What is the smallest hanging mass that will start the block moving?

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   The hanging block pulls with its weight m₂ g while the system is still at rest. Motion starts when this just exceeds the limiting friction on the table block, μ_s m₁ g. So the hanging mass must just exceed μ_s m₁, that is 0.3 × 4 or 1.2 kg. At exactly 1.2 kg, limiting friction still holds the block.