Two objects with masses 5.60 and 2.40 hang 0.600m above the floor from the ends of a cord 8.00m long passing over a frictionless pulley. Both objects start from rest.Find the maximum height reached by the 2.40kg object
To find the maximum height reached by the 2.40 kg object, you can use the principle of conservation of mechanical energy. The mechanical energy of a system is the sum of the kinetic energy and the potential energy.
Let's break down the steps to calculate the maximum height reached by the object:
1. Determine the potential energy at the starting position:
- The starting position is when the 2.40 kg object is at its lowest point, 0.600 m above the floor.
- The potential energy at this position can be calculated using the formula: mgh, where m is the mass (2.40 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (0.600 m).
Potential energy at the starting position = 2.40 kg * 9.8 m/s² * 0.600 m
2. Determine the velocity of the system at the starting position:
- Since both objects start from rest, the initial velocity of the system is zero.
3. Determine the potential energy at the maximum height:
- At the maximum height, the 2.40 kg object will have no kinetic energy, and all its energy will be in the form of potential energy.
- The potential energy at the maximum height will be equal to the potential energy at the starting position.
- Use the formula: mgh, where m is the mass (2.40 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the maximum height reached.
Potential energy at the maximum height = 2.40 kg * 9.8 m/s² * h
4. Equate the potential energies at the starting position and maximum height:
- Setting the potential energies at both positions equal, we can solve for the maximum height.
2.40 kg * 9.8 m/s² * 0.600 m = 2.40 kg * 9.8 m/s² * h
5. Solve the equation to find the maximum height:
- Divide both sides of the equation by (2.40 kg * 9.8 m/s²) to isolate h:
0.600 m = h
Therefore, the maximum height reached by the 2.40 kg object is 0.600 m.