A pendulum consists of an object of mass 1.07 kg that hangs at the end of a massless bar, a distance 1.14 m from the pivot point. Calculate the magnitude of the torque due to gravity about the pivot point if the bar makes an angle of 22° with the vertical.
the weight will be mgCos22 in the direction perpendicular to the bar.
So torque will be weightpendulum*cos22*1.14
will the weight be in kg or grams?
It does not matter IF you put your units on the problem. However, if your weight is in Newtons, you better use kg as masses.
To calculate the magnitude of the torque due to gravity about the pivot point, we can use the formula:
Torque = m * g * r * sin(θ)
Where:
m = mass of the object (1.07 kg)
g = acceleration due to gravity (9.8 m/s^2)
r = distance from the pivot point to the center of mass (1.14 m)
θ = angle between the bar and the vertical (22°)
Now, let's plug in the values and calculate the torque:
Torque = (1.07 kg) * (9.8 m/s^2) * (1.14 m) * sin(22°)
To find the sine of 22°, we can use a scientific calculator or an online calculator.
The sine of 22° is approximately 0.3746.
Torque = (1.07 kg) * (9.8 m/s^2) * (1.14 m) * 0.3746
Simplifying this calculation:
Torque ≈ 4.427 N⋅m
Therefore, the magnitude of the torque due to gravity about the pivot point is approximately 4.427 N⋅m.