a 100 kg block being released from rest over a pulley from a height of 1.0 m. It takes 0.98 s to reach the floor. What is the mass of the block hanging on the other side of the pulley.

To find the mass of the block hanging on the other side of the pulley, we can use the concept of conservation of energy.

The potential energy (PE) that the 100 kg block initially has due to its height is given by:

PE = mgh

where m is the mass (100 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (1.0 m).

PE = (100 kg)(9.8 m/s^2)(1.0 m)
PE = 980 J

Since the block is released from rest, the initial kinetic energy (KE) is zero.

When the block reaches the floor, it has converted all its potential energy into kinetic energy. Therefore, the final kinetic energy (KE) can be calculated using the equation:

KE = (1/2)mv^2

where m is the mass of the hanging block, and v is the velocity of the falling block just before it reaches the floor.

To calculate the velocity (v), we can use the equation of motion:

v = u + gt

where u is the initial velocity (zero in this case), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to reach the floor (0.98 s).

v = 0 + (9.8 m/s^2)(0.98 s)
v = 9.604 m/s

Now we can substitute the values into the kinetic energy equation to find the mass (m) of the hanging block:

KE = (1/2)m(9.604 m/s)^2
980 J = (1/2)m(9.604 m/s)^2

Solving for m:

m = (2)(980 J) / (9.604 m/s)^2
m ≈ 204 kg

Therefore, the mass of the block hanging on the other side of the pulley is approximately 204 kg.

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