How is Torque Calculated for a Mouse on a Clock Hand?

[Lance WIlliam]

A 55g mouse runs out to the end of the 17cm -long minute hand of a grandfather clock when the clock reads 10 minutes past the hour.

What torque does the mouse's weight exert about the rotation axis of the clock hand?
in Nm

Im using the eqn. (torque)=rFsin(theta)
I put

(torque)=(.17m)(.539the mg)sin(150) and I am wrong...I think its the angle or the force...

The mouses weight should be Mg right? since its the only acting force?
And if a clock is at 2 then its 30 degree above the horizontal and thaking the angle perpendicualr to that is 150 degrees...
I d K...

 

[Doc Al]

Looks right to me. Why do you think it's wrong?

 

[Lance WIlliam]

well my answer is .09 Nm and it says I am wrong...

 

[Doc Al]

well my answer is .09 Nm and it says I am wrong...

Redo your calculation. The formula you had before looked OK to me, but that answer does not.

 

[Lance WIlliam]

I got 4.58e-2...still wrong..I don't see what I am doing wrong?

 

[Doc Al]

I got 4.58e-2...still wrong..I don't see what I am doing wrong?

That looks OK to me. Do they want you to include direction? (Like clockwise or counterclockwise?) Those online systems can be picky (and sometimes wrong).

 

[Lance WIlliam]

NOpe they just want it in N m...I hate online homework...thanks for your help.

 

[alphysicist]

Hi Lance WIlliam,

A 55g mouse runs out to the end of the 17cm -long minute hand of a grandfather clock when the clock reads 10 minutes past the hour.

What torque does the mouse's weight exert about the rotation axis of the clock hand?
in Nm

Im using the eqn. (torque)=rFsin(theta)
I put

(torque)=(.17m)(.539the mg)sin(150) and I am wrong...I think its the angle or the force...

The mouses weight should be Mg right? since its the only acting force?
And if a clock is at 2 then its 30 degree above the horizontal and thaking the angle perpendicualr to that is 150 degrees...
I d K...

The minute hand is 30 degrees above the horizontal, so that's right. However, I don't believe the sin(150 degrees) in your equation is correct. Do you see what it needs to be?

 

[Doc Al]

The minute hand is 30 degrees above the horizontal, so that's right. However, I don't believe the sin(150 degrees) in your equation is correct. Do you see what it needs to be?

At 10 minutes past the hour, the minute hand will be 30 degrees to the right of the vertical or 60 degrees above the horizontal (making the angle between "r" and "F" 150 degrees). Or did I misread the problem?

 

[Lance WIlliam]

if its 10past past the hour its at 2 on the clock so since 3 is a horizontal on the clock the minute hand its 30degrees above it.In toque the (theta) used is the angle between the r vector and the F vector thus they are perpendicular to each other...I get 150 degrees...maybe I am doing it wrong...

 

[alphysicist]

Hi Doc Al,

At 10 minutes past the hour, the minute hand will be 30 degrees to the right of the vertical or 60 degrees above the horizontal (making the angle between "r" and "F" 150 degrees). Or did I misread the problem?

At 10 minutes past the hour, the minute hand has made 1/6 of a revolution, so I believe it's 60 degrees from the vertical.

 

[Doc Al]

At 10 minutes past the hour, the minute hand has made 1/6 of a revolution, so I believe it's 60 degrees from the vertical.

D'oh! You're right, of course. I was thinking of the minute hand pointing to 1 o'clock, which is 5 minutes past the hour.

(Good thing I use a digital watch!)

 

[Doc Al]

if its 10past past the hour its at 2 on the clock so since 3 is a horizontal on the clock the minute hand its 30degrees above it.In toque the (theta) used is the angle between the r vector and the F vector thus they are perpendicular to each other...I get 150 degrees...maybe I am doing it wrong...

Yes, the r vector is 30 degrees above the horizontal, but the F vector (the weight of the mouse) points down and is thus 90 degrees below the horizontal. They are not perpendicular. (And if they were, that would be 90 degrees, not 150!)

Given that, what's the angle between r and F?

 

[Lance WIlliam]

I get 60 degree as my angle between the two vectors

 

[Doc Al]

I get 60 degree as my angle between the two vectors

That will work fine, for your purpose. (Since \sin\theta = \sin(180 - \theta).)

But I'd say to draw yourself a picture. The r vector is 30 degrees above the horizontal, while F is 90 degrees below. What would the angle be between those two vectors?

 

[Lance WIlliam]

THANKYOU for your Help! :)

 

[Doc Al]

You are most welcome!

Thanks to alphysicist for catching the error.