Can some one please help me with this question?
An iron bolt of mass 121.1 g hangs from a string 1.2 m long. The top end of the string is fixed. Without touching it, a magnet attracts the bolt so that it remains stationary, but is displaced horizontally 0.28 m to the right from the previously vertical line of the string. Find the magnitude of the magnetic force on the bolt.
Thank You
To find the magnitude of the magnetic force on the bolt, we can use the concept of equilibrium.
First, let's identify the forces acting on the bolt. There are two main forces: gravity (weight) and the magnetic force.
1. Weight:
The weight of the bolt can be calculated using the formula: weight = mass × acceleration due to gravity.
Therefore, weight = 121.1 g × 9.8 m/s² (mass is given in grams since it is mentioned as 121.1 g in the question).
Let's convert the mass to kilograms to maintain consistent units: weight = 0.1211 kg × 9.8 m/s² = 1.18778 N.
2. Magnetic force:
The magnetic force is responsible for keeping the bolt stationary when it is displaced. Since the bolt is displaced horizontally, we can assume that the magnetic force is the only horizontal force acting on it. This force acts in the opposite direction to keep the bolt in equilibrium.
Now, we can calculate the magnitude of the magnetic force on the bolt using the concept of equilibrium. In equilibrium, the sum of all forces acting on an object is zero.
The horizontal component of the magnetic force must balance the horizontal component of the weight. Thus, the magnitude of the magnetic force is equal to the horizontal component of the weight.
The horizontal component of the weight is given by the formula: horizontal component of weight = weight × cosine(θ), where θ is the angle between the weight vector and the horizontal line.
Since the bolt hangs vertically down, the gravity force vector is already perpendicular to the horizontal line. Therefore, the angle (θ) between the weight vector and the horizontal line is 90 degrees.
So, cosine(90) = 0.
Now, we can calculate the magnitude of the magnetic force:
Magnetic force = horizontal component of weight = 1.18778 N × 0 = 0 N.
Hence, the magnitude of the magnetic force on the bolt is 0 N.