A simple pendulum consits of a 3.0 kg point mass hanging at the end of a 2.0 long light string that is connected to a pivot point.

a. Calculate the magnitude of the torque (due to the force of gravity) around this pivot point when the string makes a 5 degree angle with the vertical.
b. Repeat this calculation for an angle of 15 degrees.

Torque= mgl *sinTheta, where theta is 90+ your angle. Draw a sketch and confirm that. I did it in my head.

24.6

To calculate the magnitude of the torque in a simple pendulum, we can use the formula:

Torque = mgl * sin(θ)

where:
m = mass of the point mass (3.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
l = length of the light string (2.0 m)
θ = angle made by the string with the vertical

a. Angle = 5 degrees
θ = 90 degrees + 5 degrees = 95 degrees

Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(95 degrees)

To calculate the sine of 95 degrees, we need to convert it to radians:
95 degrees * (π/180) radians/degree = 1.658 radians

Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(1.658 radians)
= 117.6 N∙m

Therefore, the magnitude of the torque when the string makes a 5-degree angle with the vertical is 117.6 N·m.

b. Angle = 15 degrees
θ = 90 degrees + 15 degrees = 105 degrees

Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(105 degrees)

To calculate the sine of 105 degrees, we need to convert it to radians:
105 degrees * (π/180) radians/degree = 1.832 radians

Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(1.832 radians)
= 202.8 N∙m

Therefore, the magnitude of the torque when the string makes a 15-degree angle with the vertical is 202.8 N·m.

To calculate the magnitude of the torque acting on a simple pendulum due to the force of gravity, you can use the equation:

Torque = mgl * sin(θ)

where:
m = mass of the point mass (3.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
l = length of the string (2.0 m)
θ = angle made by the string with the vertical

Here's how you can calculate the magnitude of the torque for each given angle:

a. When the string makes a 5-degree angle with the vertical:
θ = 90° + 5° = 95°
Plugging the values into the formula:
Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(95°)

b. When the string makes a 15-degree angle with the vertical:
θ = 90° + 15° = 105°
Plugging the values into the formula:
Torque = (3.0 kg) * (9.8 m/s^2) * (2.0 m) * sin(105°)

To calculate the sine of an angle, you can use a scientific calculator or an online trigonometric calculator. Make sure to set your calculator to degree mode before finding the sine value.

Remember, it's always a good practice to draw a sketch or diagram to visualize the problem and confirm the angles and calculations.

a. 5.125 Nm