An iron bolt of mass 65g hangs straight down from a string 35.7cm long. Without touching it, a magnet attracts the bolt so that it remains stationary, but is displaced horizontally 28.0cm to the right from the previously vertical line of the string. The magnet is located to the right of the bolt and on the same vertical level as the bolt in the final configuration. (a) Find the tension in the string. (b) Find the magnetic force on the bolt.
Assuming θ is the angle between the initial and the final position of the string , sin(θ) = 28/35.7 and cosθ = 0.619
Drawing a free body diagram for the bolt, we have tension in the direction of the string, weight which is acting downwards and the magnetic force which is acting to the right. Therefore,
Along the y axis we have, Tcosθ=mg
from which we can find the tension T
Along the x axis we have , F=Tsinθ
where F is the magnetic force on the bolt.