Question

A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 5.0 angle with the vertical. (b) Does the torque increase or decrease as the angle increases? Explain.

Answer 1

a)τ= 5.1156 N-m

b)As the sin increases with increase in θ , hence torque will increase on increase θ.

Explanation:

a)

Torque T = r * f * sin θ

= rmgsinθ

=2.0 m * 3.0 kg * 9.8 m/s^2 * sin 5 °

sin 5 degree =0.087

= 2.0 m * 3.0 kg * 9.8 m/s^2 * 0.087

τ= 5.1156 N-m

b)

increases

As the sin increases with increase in θ , hence torque will increase on increase θ.

Answer 2

(a) The torque on the object is 5.124 Nm

(b) The torque increases with an increase in angle.

Simple pendulum:

(a) The torque on the object is given by:

τ = rFsinθ

where r = 2m is the distance of the object from the axis

F = mg is the force acting on it, and

θ is the angle between r and F

So,

$\tau=2\times 3\times9.8\times sin5\\\\\tau=5.124\;Nm$

(b) As we saw in the previous part, the torque is given by:

τ = rFsinθ

τ ∝ sinθ

This means the torque increases with an increase in the angle, and it is maximum at θ = 90°. Basically, it varies between maximum and minimum as a sine function.

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