An iron bolt of mass 80.0 g hangs from a string 38.8 cm long. The top end of the string is fixed. Without touching it, a magnet attracts the bolt so that it remains stationary, displaced horizontally 28.0 cm to the right from the previously vertical line of the string.

(a) Find the tension in the string.
(b) Find the magnetic force on the bolt.

This is a duplicate post and has been answered elsewhere

To find the tension in the string, we can start by calculating the force due to gravity acting on the bolt. We can then use this information to find the tension in the string.

(a) Calculate the force due to gravity:
The force due to gravity can be calculated using the formula:

F_gravity = m * g

Where:
m = mass of the bolt (in kg)
g = acceleration due to gravity (approximately 9.8 m/s²)

Convert the mass of the bolt from grams to kilograms:

m = 80.0 g / 1000 = 0.08 kg

Calculate the force due to gravity:

F_gravity = 0.08 kg * 9.8 m/s² = 0.784 N

(b) Find the tension in the string:
Now that we know the force due to gravity, we can find the tension in the string by analyzing the forces acting on the bolt. In equilibrium, the tension in the string must be equal to the force due to gravity.

Since the bolt is displaced horizontally to the right, there must also be a magnetic force acting on it that counteracts the force due to gravity. The tension in the string will be the vector sum of these forces.

To find the magnetic force on the bolt, we need to use the fact that the bolt remains stationary when attracted by the magnet. This implies that the magnetic force acting on the bolt must be equal and opposite to the force due to gravity.

Therefore, the tension in the string is equal to the force due to gravity:

Tension = F_gravity = 0.784 N