A 100 kg block is hanging from a frictionless pulley with another block of unknown mass on the other side of the pulley. It is released from a height of 1 meter above the ground. It then takes 0.9 seconds to reach the ground. What is the weight of the other mass?
To find the weight of the other mass, we need to use the principle of conservation of energy. The total energy of the system remains constant throughout the motion, so we can equate the initial energy to the final energy.
Let's consider the different forms of energy involved in this system:
1. Gravitational Potential Energy: This is the energy due to the height of the blocks above the ground. It can be calculated using the formula: Potential Energy = mass x gravity x height.
2. Kinetic Energy: This is the energy due to the motion of the blocks. It can be calculated using the formula: Kinetic Energy = 0.5 x mass x velocity^2.
3. With the information given, we know that the acceleration of the system is g (acceleration due to gravity) because the pulley is frictionless.
Initially, the 100 kg block has gravitational potential energy equal to Potential Energy = 100 kg x gravity x 1 m (height above the ground).
When the block reaches the ground, all of its potential energy will have been converted into kinetic energy. So, we can equate the initial potential energy to the final kinetic energy.
100 kg x gravity x 1 m = 0.5 x (100 kg + unknown mass) x velocity^2
Now, we need to find the velocity at the point the block reaches the ground. We can use the formula: velocity = acceleration x time. Since the acceleration is g (gravity), we have velocity = g x time = g x 0.9 s.
Substituting this value into the equation:
100 kg x gravity x 1 m = 0.5 x (100 kg + unknown mass) x (g x 0.9 s)^2
Simplifying the equation, we can cancel out the gravity:
100 kg = 0.5 x (100 kg + unknown mass) x (0.9 s)^2
From here, we can solve for the unknown mass by isolating it on one side of the equation and solving the quadratic equation. After finding the value of the unknown mass, the weight can be determined by multiplying the mass by the acceleration due to gravity (9.8 m/s^2).