Torques on a Ruler Homework: Find Unknown Mass

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In summary, the centimeter ruler is in equilibrium and has an unknown mass at the 4.7 cm mark. The unknown mass is closer to the pivot point which means it must have more mass than 10 g.
  • #1
PeachBanana
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Homework Statement



A centimeter ruler, balanced at its center point, has two coins placed on it, as shown in the figure. One coin, of mass 10 g , is placed at the zero mark; the other, of unknown mass , is placed at the 4.7 cm mark. The center of the ruler is at the 3.0 cm mark. The ruler is in equilibrium; it is perfectly balanced.

Find the unknown mass.

Homework Equations



τ = F * r

The Attempt at a Solution



I set the zero mark to be in a center of the ruler. Then I tried to compute the counterclockwise Torque.

τ = (0.01 kg)(0.03 m)(9.8 m/s^2)

I'm really unsure about using the acceleration due to gravity. Should I have been using τ = Iα instead? I figure if I know how to properly find the counterclockwise torque, the clockwise torque will follow the same method.
 

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  • #2
No, your method is fine. The Force term is given by F=mg.

You said you put your zero point in the centre of the ruler. But the question says that the centre is at 3.0cm. Your calculation for the counterclockwise moment is still correct though, as the zero point is 3cm from the fulcrum.
 
Last edited:
  • #3
Yeah, the problem did say to put the zero mark at the end but I thought it would be easier to put it in the middle since I wouldn't have to worry about that force. Here's what I've done so far:

counterclockwise torque = (0.01 kg)(0.03m)(9.8 m/s^2)
counterclockwise torque = 0.00294 N * M

clockwise torque = (x kg)(9.8 m/s^2)(0.017 m)
0.00294 N * M (I did this because in order for the ruler to be in equilibrium the torques must cancel)= (x kg)(9.8 m/s^2)(0.017 m)

0.00294 N * M = 0.1666 1/s^2 * (x kg)
x = 0.017 kg

They want the answer in grams though so x = 1.7 g. This doesn't make sense because the second mass is closer to the pivot point which means it must have more mass than 10 g.
 
  • #4
1kg=1000g :smile:
 
  • #5
Wowowowowowowowow! Haha, I think ≈ 18 g sounds a bit better.
 

Related to Torques on a Ruler Homework: Find Unknown Mass

What is a torque?

A torque is a measure of the force that causes an object to rotate. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point of application of the force.

How can I calculate the torque on a ruler?

To calculate the torque on a ruler, you need to know the force acting on the ruler and the distance from the axis of rotation to the point where the force is applied. Then, you can use the formula torque = force * distance to calculate the torque.

What is the principle of moments?

The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the counterclockwise moments about the same point. In other words, the total torque acting on the object must be equal to zero.

How can I find the unknown mass of an object using a ruler?

To find the unknown mass of an object using a ruler, you can use the principle of moments. First, balance the ruler on a pivot point and measure the distance from the pivot point to the unknown mass. Then, add known masses to the other side of the ruler until it is balanced again. The sum of the known masses multiplied by their distances from the pivot point will be equal to the unknown mass multiplied by its distance from the pivot point. You can then solve for the unknown mass.

What are some common sources of error when determining unknown masses using a ruler?

There are a few common sources of error when determining unknown masses using a ruler. These include using an inaccurate ruler, not measuring the distance from the pivot point to the unknown mass correctly, and not balancing the ruler carefully. Additionally, friction and air resistance can also affect the accuracy of the measurements.

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