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.