A man faces difficulty while swimming in a dam - NSC Physical Sciences - Question 2 - 2022 - Paper 1

The free-body diagram should include the following forces:

• The gravitational force ( $F_g = mg$ ) acting downwards on the man-tube combination.
• The normal force (N) acting upwards from the water's surface.
• The tension (T) in the rope at an angle of 50° with the horizontal.
• The frictional force (f) acting horizontally against the direction of motion.

To find the tension in the rope, we can use the following equation based on the forces acting on the man-tube combination:

1. Resolving forces in the vertical direction: $$$$

ightarrow N = F_g = (70 + 4) imes 9.8 = 686 ext{ N}$$

2. Resolving forces in the horizontal direction: $$$$

ightarrow T imes ext{cos}(50°) = 300 ext{ N}$$

3. Solving for T: $$$$

ightarrow T ext{ is calculated as approximately } 466.79 ext{ N}.$$

If the helicopter accelerates, the net force on the man-tube combination will increase because an additional force will be needed to account for the acceleration. Hence, the tension in the rope will INCREASE. The frictional force remains constant, but the additional force needed to accelerate will result in a higher tension.

To calculate the average upward force,

1. Calculate the gravitational force acting on the tube: $F_g = m imes g = 4 imes 9.8 = 39.2 ext{ N}$

2. Determine the net force while sinking:

   • The displacement (s) is 0.8 m, and the initial speed (v_i) is 16 m/s. We can use: $v_f^2 = v_i^2 + 2a s$
   • Assume the final speed (v_f) as 0 in water:
   $$$$

ightarrow a = -160 ext{ m/s}^2$$

3. Using Newton's second law: $F_{net} = m imes a$ $F_{net} = 4 imes (-160) = -640 ext{ N}$

4. The average upward force exerted (F_upward) can be calculated as: $F_{upward} = F_g + |F_{net}| = 39.2 + 640 = 679.2 ext{ N}$