A Bob of mass M is suspended by string from the ceiling of a car movin...
Problem:
A Bob of mass M is suspended by string from the ceiling of a car moving with an acceleration a as shown figure. Find the tension in the string.
Solution:
Step 1: Identify the forces acting on the bob
In order to find the tension in the string, we need to consider the forces acting on the bob. In this case, the bob is suspended from the ceiling of a car. The two main forces acting on the bob are:
1. The gravitational force (weight) acting downwards.
2. The tension force in the string acting upwards.
Step 2: Analyze the gravitational force
The gravitational force acting on the bob can be calculated using the equation:
Weight = mass x acceleration due to gravity (W = mg)
where m is the mass of the bob and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 3: Analyze the tension force in the string
The tension force in the string can be calculated using Newton's second law of motion:
Tension = mass x acceleration
where T is the tension force, M is the mass of the bob, and a is the acceleration of the car.
Step 4: Calculate the tension in the string
To find the tension in the string, we need to substitute the values of mass and acceleration into the equation:
Tension = M x a
Step 5: Simplify the equation
Since the mass of the bob (M) is common in both the gravitational force and the tension force, we can simplify the equation:
Tension = M x (a + g)
Step 6: Substitute the values
Finally, we substitute the given values of mass (M) and acceleration (a) into the equation to find the tension in the string.
Conclusion:
The tension in the string can be calculated using the equation Tension = M x (a + g), where M is the mass of the bob, a is the acceleration of the car, and g is the acceleration due to gravity.