A simple pendulum consists of a small object of mass 7.40 kg hanging at the end of a 2.10 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 3.00° angle with the vertical
What is mg*length*cosineAngle
I got 152.08 and its saying its wrong!
M= m•g•L•sinα=7.4•9.8•2.1•sin3°=7.97 N•m
To calculate the magnitude of the torque due to the force of gravity on a simple pendulum, you need to know the weight of the object and the distance between the pivot point and the line of action of the weight force.
In this case, the weight force of the object is the force of gravity acting on it, given by the equation F = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The line of action of the weight force is perpendicular to the string, so the distance between the pivot point and the line of action is equal to the length of the string.
Given that the mass of the object is 7.40 kg and the length of the string is 2.10 m, we can calculate the weight force as follows:
F = m * g
F = 7.40 kg * 9.8 m/s^2
F = 72.52 N
The next step is to find the perpendicular distance between the pivot point and the line of action, which is equal to the horizontal component of the length of the string. This can be calculated using the equation:
r = L * sin(theta)
where r is the perpendicular distance, L is the length of the string, and theta is the angle between the string and the vertical.
In this case:
r = 2.10 m * sin(3.00°)
r = 2.10 m * 0.0523 (sin(3.00°) is approximately 0.0523)
r ≈ 0.11 m
Finally, we can calculate the torque using the equation:
τ = F * r
τ = 72.52 N * 0.11 m
τ ≈ 7.98 N*m
Therefore, the magnitude of the torque about the pivot point when the string makes a 3.00° angle with the vertical is approximately 7.98 N*m.