a) A simple pendulum consists of a small object of mass 3.3 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point.Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 4.5° angle with the vertical. __________N.m
b)Does the torque increase or decrease as the angle increase? Explain.
To calculate the torque due to the force of gravity acting on the object in a simple pendulum, we need to use the equation:
Torque = force × lever arm
In this case, the force is the weight of the object, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
where the acceleration due to gravity is approximately 9.8 m/s^2.
a) To calculate the torque, we need to find the weight of the object.
Weight = mass × acceleration due to gravity
Weight = 3.3 kg × 9.8 m/s^2
Weight = 32.34 N
Now, let's find the lever arm, which is the perpendicular distance between the pivot point and the line of action of the force. In a simple pendulum, this is equal to the length of the string.
Lever arm = 2.0 m
Now we can calculate the torque using the formula:
Torque = force × lever arm
Torque = Weight × lever arm
Torque = 32.34 N × 2.0 m
Torque = 64.68 N·m
Therefore, the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 4.5° angle with the vertical is 64.68 N·m.
b) As the angle increases, the torque will increase. This can be explained by the fact that torque is directly proportional to the lever arm, which is the perpendicular distance between the pivot point and the line of action of the force. When the angle increases, the effective length of the lever arm also increases, resulting in a greater torque.