A simple pendulum consists of a small object of mass 1.2 kg hanging at the end of a 2.07 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 an angle of 6.59 degrees with the vertical.
To calculate the magnitude of the torque (due to the force of gravity) about the pivot point, we can use the equation:
Torque = Force * Perpendicular distance
In this case, the force is the weight of the object, and the perpendicular distance is the component of the distance between the pivot point and the object that is perpendicular to the direction of the force.
1. Start by finding the weight of the object:
Weight = mass * gravity
Weight = 1.2 kg * 9.8 m/s^2
Weight = 11.76 N
2. Calculate the perpendicular distance:
Perpendicular distance = length of string * sin(angle)
Perpendicular distance = 2.07 m * sin(6.59 degrees)
Perpendicular distance ≈ 0.228 m
3. Finally, calculate the torque:
Torque = Weight * Perpendicular distance
Torque = 11.76 N * 0.228 m
Torque ≈ 2.683 N·m
Therefore, the magnitude of the torque (due to the force of gravity) about the pivot point is approximately 2.683 N·m.
To calculate the magnitude of the torque (due to the force of gravity) about the pivot point of a simple pendulum, we can use the equation:
Torque = Force × Lever Arm
In this case, the force is the weight of the object and the lever arm is the perpendicular distance between the pivot point and the line of action of the force.
Step 1: Calculate the force of gravity
The force of gravity can be calculated using the formula:
Force = mass × acceleration due to gravity
Given that the mass of the object is 1.2 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force:
Force = 1.2 kg × 9.8 m/s²
Step 2: Find the lever arm
The lever arm is the perpendicular distance between the pivot point and the line of action of the force. In this case, it is the length of the string.
Lever Arm = length of string × sin(angle with vertical)
Given that the length of the string is 2.07 m and the angle with the vertical is 6.59 degrees, we can calculate the lever arm:
Lever Arm = 2.07 m × sin(6.59°)
Step 3: Calculate the torque
Using the torque formula Torque = Force × Lever Arm, we can plug in the values we calculated:
Torque = Force × Lever Arm
Torque = (1.2 kg × 9.8 m/s²) × (2.07 m × sin(6.59°))
Now, substitute the values and calculate the torque.