Question

A simple pendulum with a length of

2.83 m and a mass of 6.54 kg is given an initial speed of
2.96 m/s at its equilibrium position. What is the tension in the string at the equilibrium position?

a. 28.9 N
b. 37.4 N
c. 45.8 N
d. 54.3 N

Answer 1

It is calculated by multiplying the mass (6.54 kg) by the acceleration due to gravity (9.80 m/s²), which equals 64.092 N, not matching any of the provided options.

Step-by-step explanation:

To determine the tension in the string of a simple pendulum at the equilibrium position, we need to consider the forces acting on the mass. At equilibrium, the only vertical force is due to the weight of the mass, which is the product of the mass and the acceleration due to gravity (g).

In mathematical terms, the weight (W) is W = m * g, where m is the mass (6.54 kg) and g is the acceleration due to gravity (9.80 m/s²). The tension in the string at the equilibrium position would be equal to the weight of the mass, since the pendulum is at rest at this point and there are no other vertical forces acting on the mass. There is no contribution from the horizontal motion to the tension, since it only affects the horizontal component.

Therefore, the tension (T) at the equilibrium position is T = m * g = 6.54 kg * 9.80 m/s² = 64.092 N. This isn't one of the provided options, but it's the correct calculation based on the given parameters.