An object of mass m is hanging by a string from the roof of an elevator. The elevator is moving downward and slowing down. What is the tension in the string?

To solve this problem, we need to understand the forces acting on the object. There are two forces acting on the object: the force of gravity pulling it down and the tension in the string pulling it up.

1. First, calculate the force of gravity (weight of the object), which is equal to the mass of the object times the acceleration due to gravity. The formula is Fg = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

2. The elevator is moving downward and slowing down, which means it is accelerating upwards. Let's denote the acceleration of the elevator as a.

3. The net force acting on the object is the difference between the tension in the string (T) and the force of gravity. Because the elevator is accelerating upwards, the net force is also upwards. According to Newton's second law (F = m * a), we can write this as T - Fg = m * a.

4. Solve the equation from step 3 for T to find the tension in the string. The formula is T = m * a + m * g.

So, the tension in the string is equal to the mass of the object times the sum of the acceleration of the elevator and the acceleration due to gravity.