Two objects with masses 4.90 and 2.10 hang 0.800 above the floor from the ends of a cord 7.20 long passing over a frictionless pulley. Both objects start from rest.

Find the maximum height reached by the 2.10 object.

The heavier object will move .8 m down, thelighter will move up an additional .8m.

max height= initial height+movement up.

I am surprised this problem was given in physics.

but how do you find the initial height?

bob, you fail to understand that the tension force has accelerated the lighter object upwards; when the heavier object hits the floor, the lighter object still has upward velocity. the magnitude of this velocity is determined by the magnitude of the tension force.

To find the maximum height reached by the 2.10 kg object, we need to analyze the forces acting on the system and apply the principles of conservation of energy.

1. Determine the gravitational forces acting on both objects:
The weight of an object is given by the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the accelerations are negligible since the objects are starting from rest. Thus, the gravitational force on the 4.90 kg object is (4.90 kg) * (9.8 m/s^2) = 48.02 N, and the gravitational force on the 2.10 kg object is (2.10 kg) * (9.8 m/s^2) = 20.58 N.

2. Determine the tension in the cord:
Since the objects are connected by the cord passing over a frictionless pulley, the tension in the cord is the same on both sides. Let's denote the tension in the cord as T.

3. Set up the equations using the principle of conservation of energy:
At the maximum height reached by the 2.10 kg object, its kinetic energy will be zero. Therefore, the sum of the potential energies of both objects must equal the initial potential energy of the system.

Potential energy is given by the formula PE = m * g * h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

For the 4.90 kg object: PE = (4.90 kg) * (9.8 m/s^2) * 0.800 m
For the 2.10 kg object: PE = (2.10 kg) * (9.8 m/s^2) * h

Since the sum of the potential energies equals the initial potential energy:
(4.90 kg) * (9.8 m/s^2) * 0.800 m + (2.10 kg) * (9.8 m/s^2) * h = (4.90 kg + 2.10 kg) * (9.8 m/s^2) * 7.20 m

4. Solve the equation for h, which represents the maximum height reached by the 2.10 kg object.