Pendulum problem - What is the magnitude of the torque?

In summary, a 0.75kg mass is attached to one end of a 1.25m long massless rod and the other end is hung from a pivot. The resulting pendulum, when at a 30 degree angle from the vertical, has a torque of 3.68N acting on it. The correct torque should be half of this value, which can be found by resolving the vector magnitude of 3.68N at a 60 degree angle and multiplying it by the length of the rod.
  • #1
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a small mass of 0.75kg is attached to one end of a 1.25m long massless rod, and the other end is hung from a pivot. When the resulting pendulum is 30degrees from the vertical what is the magnitude of the torque about the pivot?

what i did:
-Fsin30 -mg = 0
Fsin30 = -mg
F = -14.7N

t = rFsin30
t = 1.25(-14.7sin30)
t = -9.2N

the answer is supose to be half of this what did i do wrong?
 
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  • #2
I always always draw out the problem and figure it out geometrically on paper rather than resort to filling in formuals. Check out the attachment. Its easy to see from this that you need to find the vector mag. that acts on the tangent of the rods arc. Get the angle. Its 60. Get the resolved vector magnitude.

cos 60= F/7.36

Torque = 3.68 x 1.25
=4.6 Nm

Was your diagram maybe screwed up?>?
 

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Your calculations for the magnitude of the torque seem to be correct. However, the given answer of half of your result may be due to the fact that the problem is asking for the magnitude of the torque, which is a scalar quantity. This means that the direction of the torque does not matter, only its magnitude. Therefore, the negative sign in your answer can be ignored and the magnitude of the torque would be 9.2N, which is half of the force you calculated. Alternatively, if the problem is asking for the net torque (taking into account the direction), then your answer would be correct. It is important to clarify what the problem is asking for in order to provide an accurate response.
 
1.

What is a pendulum problem and why is the magnitude of torque important?

A pendulum problem is a physics concept that involves a suspended mass attached to a fixed point by a string or rod. It is important to understand the magnitude of torque in a pendulum problem because it determines the amount of rotational force acting on the pendulum, which affects its motion.

2.

How is torque calculated in a pendulum problem?

The torque on a pendulum is calculated by multiplying the force applied to the pendulum by the distance from the pivot point to the point where the force is applied. This can be represented by the equation τ = Fd, where τ is torque, F is force, and d is distance.

3.

What factors affect the magnitude of torque in a pendulum problem?

The magnitude of torque in a pendulum problem is affected by the length of the pendulum, the mass of the suspended object, and the angle at which the pendulum is released. Other factors that can affect torque include air resistance and friction.

4.

How does the magnitude of torque affect the motion of a pendulum?

The magnitude of torque determines the speed and direction of a pendulum's motion. A larger torque will result in a faster swinging pendulum, while a smaller torque will result in a slower swinging pendulum. The direction of the torque will also determine the direction of the pendulum's swing.

5.

Can the magnitude of torque be changed in a pendulum problem?

Yes, the magnitude of torque in a pendulum problem can be changed by altering the length of the pendulum, the mass of the suspended object, or the angle at which the pendulum is released. Changing these factors will result in a different amount of force being applied to the pendulum, thus affecting the magnitude of torque.

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