Two boxes are connected by a cord running over a pulley. Box A is on a table and Box B is hanging off of the pulley. The system is released from rest and Box B drops a distance D.

What is the word done by gravity on box B?

is it W=Mass of B X g X D?

yes

force of gravity = m g
distance = D
work done by gravity = m g D

Remember the tension in the cord also does work, but that was not asked.

The work done by gravity on box B can be determined using the formula:

Work = Force × Distance

In this case, the force applied by gravity is the weight of box B, which can be calculated using the equation:

Weight = mass × acceleration due to gravity

The mass of box B may be denoted as m, and the acceleration due to gravity is typically represented as g.

Therefore, the weight of box B is given by:

Weight = m × g

The distance traveled by box B is D. Hence, the work done by gravity on box B is:

Work = Weight × Distance
= m × g × D

Therefore, the work done by gravity on box B is m × g × D.

To calculate the work done by gravity on Box B, you need to know the mass of Box B and the distance it has dropped.

The work done by gravity can be determined using the formula:

Work = Force x Distance x Cos(θ)

In this case, the force is the gravitational force acting on Box B, which is equal to the weight of Box B.

Weight = Mass x Acceleration due to gravity

Since the system is released from rest, Box B is accelerated downward by gravity. The acceleration due to gravity is approximately 9.8 m/s².

Now, let's assume the mass of Box B is M. The weight of Box B can be calculated as:

Weight = M x 9.8

Next, you need to calculate the distance Box B has dropped. According to the problem, the distance dropped is D.

Finally, you need to calculate the angle θ between the force vector and the direction of motion. In this case, the gravitational force is acting vertically downward, and the displacement of Box B is also vertically downward. Therefore, the angle θ is 0°, and cos(0°) equals 1.

Now, plug in the values into the formula:

Work = (M x 9.8) x D x Cos(0°)
= M x 9.8 x D x 1
= M x 9.8 x D

So, the work done by gravity on Box B is equal to M x 9.8 x D.