Let's analyze and solve each part of this problem.

Given Data:

• Mass of the block, $m = 0.038 \, \text{kg}$
• Radius of the loop, $R = 14 \, \text{cm} = 0.14 \, \text{m}$
• Height $h = 5R = 5 \times 0.14 = 0.7 \, \text{m}$

Approach

1. Kinetic and Potential Energy at Point Q: Since the track is frictionless, we can use energy conservation to find the speed of the block at point $Q$, which will help determine the forces acting on the block.

2. Circular Motion at Point Q: At point $Q$, the block is moving along a circular path, so it will experience a centripetal force directed toward the center of the loop. This centripetal force will depend on the velocity we calculate using energy conservation.

Step-by-Step Solution

Part (a): Horizontal Component of the Net Force at Point Q

1. Use Conservation of Energy:

   • Total mechanical energy at the top (point $P$) is: $E_{\text{top}} = mgh$
   • Total mechanical energy at point $Q$ is: $E_Q = mg(2R) + \frac{1}{2}mv_Q^2$
   • Setting $E_{\text{top}} = E_Q$ and solving for $v_Q$.

2. Calculate Horizontal Force Component.

Part (b): Vertical Component of the Net Force at Point Q

Using similar steps but focusing on the vertical force component calculation.

Part (c): Height for Block to Lose Contact at Top of Loop

The condition for losing contact at the top of the loop means the normal force is zero. We can set up the equations to find the required height for that condition.

Would you like the detailed calculation for each part?

Here are some related questions:

1. How is energy conservation applied in frictionless motion scenarios?
2. What role does centripetal force play in circular motion?
3. How does one calculate the normal force in circular motion?
4. What are the conditions for an object to lose contact in a loop-the-loop scenario?
5. How can energy principles help determine motion in non-linear paths?

Tip: In problems involving circular motion and conservation of energy, always check if forces need to satisfy the centripetal requirement at each point.