In a Cavendish balance apparatus suppose that M1= 1.10Kg, M2= 25.0Kg, and the rod connecting the M1 pairs is 30.0cm long. If, in each pair, M1 and M2 are 12.0cm apart center-to-center, find (a) the net force and (b) the net torque (about the rotation axis) on the rotating part of the apparatus. (c) Does is seem that the torque in part (b) would be enough to easily rotate the rod? Suggest some ways to improve the sensitivity of this experiment.
You can use Newtons equation to find the force of attraction.
Then, torque=2*force*15cm
To find the net force and net torque in the Cavendish balance apparatus, we need to consider the gravitational forces acting on the masses M1 and M2.
(a) Net Force:
The net force is the vector sum of the gravitational forces acting on the masses M1 and M2. We can calculate it using the formula:
F = G * (M1 * M2) / r^2
Where:
- F is the force between the masses (net force)
- G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2)
- M1 and M2 are the masses (1.10 kg and 25.0 kg, respectively)
- r is the separation between the centers of M1 and M2 (12.0 cm = 0.12 m)
Plugging in the values, we have:
F = (6.67430 × 10^-11 N m^2/kg^2) * (1.10 kg * 25.0 kg) / (0.12 m)^2
Calculating this expression will give you the net force.
(b) Net Torque:
The net torque is the rotational force experienced by the rotating part of the apparatus due to the unequal gravitational forces acting on M1 and M2. The torque is given by the formula:
τ = F * r
Where:
- τ is the torque
- F is the net force calculated in part (a)
- r is the distance between the line of action of the force and the rotation axis (30.0 cm = 0.30 m)
Calculating this expression will give you the net torque.
(c) Sensitivity of the Experiment:
To improve the sensitivity of the experiment, you can consider the following approaches:
1. Increase the length of the rod: A longer rod would increase the lever arm and therefore amplify the torque for a given net force.
2. Use more massive objects: Increasing the masses of M1 and M2 would increase the force between them and, consequently, the net force and torque.
3. Increase the separation distance: If possible, increase the distance between the centers of M1 and M2. This would increase the lever arm and amplify the torque.
4. Reduce external disturbances: Minimize vibrations, air currents, and other external factors that could affect the accuracy of the experiment.
Implementing these suggestions would enhance the sensitivity of the Cavendish balance apparatus, making it easier to detect and measure small torques.