Question

Consider a child who is swinging. As she reaches the lowest point in her swing:

a. the tension in the rope is equal to her weight.
b. the tension in the rope is equal to her mass times her acceleration.
c. her acceleration is downward at 9.8 m/s2.
d. none of the above.

Answer 1

None of the above. The tension in the rope is equal to the sum weight and mass times acceleration. Acceleration of the child points upwards toward the center of the motion.

Step-by-step explanation:

The child is in a centripetal motion. As a result, acceleration of the child would point towards the center of the swing.

When the child is at the lowest point of the swing, the center of the swing is right above the child. Hence, the acceleration of the child would point directly upwards.

The weight of the child points downwards at all time.

Tension in the rope always point along the rope towards the center of the swing. Because the child is at the lowest point of the swing, the rope would be vertical, and tension in the rope would point upwards.

Both tension from the rope and weight are in the vertical direction. However, because weight points downwards while tension points upwards, magnitude of the resultant net force would be the difference between the magnitude of tension and magnitude of weight.

At the same time, the resultant force on the child is nonzero because it is equal to mass times acceleration (both are nonzero). Thus:

`(\text{net force}) = (\text{tension}) - (\text{weight})`.

`(\text{tension}) = (\text{net force}) + (\text{weight})`.

Therefore, the tension in rope would be equal to neither weight nor mass times acceleration, but the sum of the two.