Question

A horizontal meter stick has a mass of 211 g. Three weights ride on the meter stick: 267 g at 49.5 cm, 199 g at 80.3 cm, and 207 g at 98.7 cm. At what location on the meter stick would the system be in balance if it were suspended there?

Answer 1

To find the location on the meter stick where the system would be in balance when suspended, you need to calculate the torques for each weight and set the sum of the torques equal to zero.

Step-by-step explanation:

To find the location on the meter stick where the system would be in balance when suspended, we need to calculate the torque of each weight and set the sum of the torques equal to zero. The formula for torque is given by the product of the weight and the distance from the fulcrum.

1. Calculate the torque for each weight:
   
   Torque₁ = (267 g) * (49.5 cm)
   
   Torque₂ = (199 g) * (80.3 cm)
   
   Torque₃ = (207 g) * (98.7 cm)
2. Set the sum of the torques equal to zero:
   
   Torque₁ + Torque₂ + Torque₃ = 0
3. Solve for the unknown location:
   
   Let x be the unknown location. The equation becomes:
   
   (267 g) * (49.5 cm) + (199 g) * (80.3 cm) + (207 g) * (98.7 cm) = (211 g) * x
4. Solve for x:
   
   x = ((267 g) * (49.5 cm) + (199 g) * (80.3 cm) + (207 g) * (98.7 cm)) / (211 g)

Calculating the expression will give you the location, in centimeters, on the meter stick where the system would be in balance when suspended.