What is the mass of the baseball bat?

[kopinator]

A baseball bat balances 69.4 cm from one end. If an 0.544 kg glove is attached to that end, the balance point moves 23.1 cm toward the glove. Calculate the mass of the bat.


sum of all touques=0
sum of all forces=0
T(torque)=r x F where r and F are vectors
T= Iα

The only thing I know about this question is that I'll be working with the torques but I don't know where to go from there.

 

[rude man]

Sum torques about the new balance point.

 

[bigfooted]

Draw a simplified picture. Always draw a picture, with the forces, moments, etc. But think about what is important and what not. There is no need to add the force acting on the balancing point for instance.

In the simplified picture you will have only mass m1 a distance x1 on the left and mass m2 a distance m2 on the right. When you add the glove to the left, you increase the mass m1 to m1+0.544 kg.
the distance x1 is reduced to x1-0.231 m.

From this information you can get an equation with x2 and m2 eliminated.

What remains is to eliminate x1 and calculate the mass m1. Think about how to eliminate x1.
If you can't find out how to eliminate x1, try two different 'made up' values of x1 to see if you can find the pattern.

 

[rude man]

There are only two masses (weights) and two lever arms involved in a single sum-of-torques equation.

 

[Nickie]

Based on the given information, we can use the equation for torque (T= r x F) to solve for the mass of the bat. We know that the bat balances at 69.4 cm from one end, and when the 0.544 kg glove is attached, the balance point moves 23.1 cm towards the glove. This means that the distance from the new balance point to the end of the bat is (69.4 - 23.1) = 46.3 cm.

Since the sum of all torques must be equal to zero, we can set up the equation as follows:

(0.544 kg)(23.1 cm) = (m bat)(46.3 cm)

Solving for the mass of the bat (m bat), we get:

m bat = (0.544 kg)(23.1 cm) / (46.3 cm) = 0.271 kg

Therefore, the mass of the baseball bat is approximately 0.271 kg.