Grandfather clock torque homework

In summary, a 55 g mouse exerts a torque of 0.094 Nm about the rotation axis of the clock hand when it runs to the end of the 17 cm long hand at 10 minutes past the hour. This is calculated using the formula Torque = rFsin(theta), where F is the weight of the mouse (0.55 N), r is the radius of the clock hand (0.17 m), and theta is the angle between the force and the radius (60 degrees).
  • #1
mvl46566
3
0

Homework Statement


A 55 g mouse runs out to the end of the 17cm long hand of an old grandfather clock when the clock reads 10min past the hour. What torque does the mouse exert about the rotation axis of the clock hand.


Homework Equations



Torque=rFsin(theta)

The Attempt at a Solution



The force acting on the mouse is his weight, so F=mg which turns out to be .55N. The radius, in meters, is .17m. Here's the tricky part, theta describes the angle between the force and the radius, so, if it is 10 past the hour, the long hand is making a 30 degree angle with the x-axis (or the 3 on a clock). The force, long hand, and x-axis make a 90 degree angle so if the angle the long hand makes with the axis is 30 degrees and the angle force makes with the axis is 90 degrees then theta must equal 60 degrees.

That is my logic but I am not sure how sound it is. If anyone can help confirm or deny this it would be much appreciated!
 
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  • #2


Yup, your reasoning is sound.
 
  • #3


I would first like to commend your approach to solving this problem. It is important to carefully consider all the variables and angles involved in order to come up with an accurate solution. Your logic seems sound, but I would suggest double checking your calculations just to be sure. Also, it may be helpful to draw a diagram to visualize the situation and confirm your reasoning about the angles involved. Overall, your approach is a good example of the scientific method in action. Keep up the good work!
 

Related to Grandfather clock torque homework

1. What is torque in relation to a grandfather clock?

Torque refers to the rotational force that is applied to the hands and gears of a grandfather clock. It is the amount of force required to keep the clock mechanisms moving and keep accurate time.

2. How do you calculate the torque of a grandfather clock?

The torque of a grandfather clock can be calculated using the equation: torque = force x distance. In the case of a grandfather clock, the force is the weight of the pendulum and the distance is the length of the pendulum.

3. Why is torque important in a grandfather clock?

Torque is important in a grandfather clock because it determines how much energy is needed to keep the clock running. If there is not enough torque, the clock will not keep accurate time and may stop running altogether.

4. What factors can affect the torque of a grandfather clock?

The length and weight of the pendulum, the number of gears in the clock's mechanism, and the condition of the clock's components can all affect the torque of a grandfather clock. Changes in temperature and humidity can also affect the torque.

5. How can you adjust the torque of a grandfather clock?

The torque of a grandfather clock can be adjusted by changing the length of the pendulum or by adding or removing weights from the clock. It is important to consult a professional clockmaker for proper adjustments to ensure the clock continues to keep accurate time.

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