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 determine the weight of the other mass, we need to use the principle of conservation of mechanical energy.
First, let's consider the initial situation when the block is released. It has gravitational potential energy due to its height above the ground. The formula for gravitational potential energy is:
Potential energy = mass × gravitational acceleration × height
Given that the mass of the block is 100 kg and the height is 1 meter, and the gravitational acceleration is approximately 9.8 m/s², we can calculate the initial potential energy.
Potential energy = 100 kg × 9.8 m/s² × 1 m
Potential energy = 980 joules
Now, let's consider the final situation when the block reaches the ground. At this point, all the potential energy has been converted to kinetic energy. The formula for kinetic energy is:
Kinetic energy = 0.5 × mass × velocity²
We need to find the velocity at the moment the block reaches the ground. We know that it takes 0.9 seconds to reach the ground, so we can calculate the velocity using the formula:
Velocity = distance / time
The distance is the height from which the block is dropped: 1 meter. So:
Velocity = 1 m / 0.9 s
Velocity ≈ 1.11 m/s
Now we can calculate the final kinetic energy. Since the block does not have any mass, we can use the equation:
Kinetic energy = mass × velocity²
Given that the mass of the block on the other side of the pulley is unknown, let's call it M. Therefore:
Final kinetic energy = M × 1.11²
According to the principle of conservation of mechanical energy, the initial potential energy must be equal to the final kinetic energy. Therefore:
980 joules = M × 1.11²
Now we can solve for M to get the weight of the other mass:
M = 980 joules / (1.11 m/s)²
Calculating this, we find:
M ≈ 793 kg
So, the weight of the other mass is approximately 793 kg.