Question

A simple pendulum consists of a massless tether 50 cm in length connected to a pivot and a small mass of 1.0 kg attached at the other end. What is the torque about the pivot when the pendulum makes an angle of 40° with respect to the vertical?

a) 2.45 Nm
b) 3.14 Nm
c) 1.87 Nm
d) 2.00 Nm

Answer 1

To calculate the torque on a simple pendulum making a 40-degree angle with the vertical, the gravitational force acting on the angle in radians and the length of the tether are used to apply the torque formula, resulting in a torque of approximately 2.45 Nm.

Step-by-step explanation:

The question relates to the concept of torque in a simple pendulum setting. To calculate the torque about the pivot when the pendulum makes an angle of 40° with the vertical, we use the formula τ = rFθ, where τ is torque, r is the length of the tether, F is the force (in this case, the component of the gravitational force acting along the arc, which can be found by F = mgθ), and θ is the angle in radians. First, we convert the angle to radians (40° ≈ 0.698 radians), then we calculate the force perpendicular to the tether (F = (1 kg)(9.8 m/s²)θ). The length of the tether is given as 0.50 m. Plugging these into the equation gives: τ = (0.50 m)(1 kg)(9.8 m/s²)sin(0.698) ≈ 2.45 Nm.