A cart of mass M1 = 6 kg is attached to a block of mass M2 = 3 kg by a string that passes over a frictionless pulley. The system is initially at rest and the table is frictionless. After the block has fallen a distance h = 1 m:
What is the work Ws done on the cart by the string?
(The cart is on the table connected to a pulley from which a block is hanging)
To find the work done on the cart by the string, we need to calculate the change in potential energy of the block and the cart.
The potential energy of an object is given by the equation:
Potential Energy = Mass x Gravity x Height
For the block:
Potential Energy of the block = (M2 x g x h)
Since the block is connected to the cart by a string passing over a pulley, the cart will move an equal distance, h, in the opposite direction to the block. Therefore, the change in height for the cart is also h.
For the cart:
Change in potential energy of the cart = - (M1 x g x h)
The negative sign is present because the cart moves in the opposite direction to the block.
Now, the work done on an object is equal to the change in its potential energy:
Work (Ws) = - (Change in Potential Energy of the Cart)
Substituting the values into the equation:
Ws = - (M1 x g x h)
Given:
M1 = 6 kg (mass of the cart)
M2 = 3 kg (mass of the block)
g = 9.8 m/s^2 (acceleration due to gravity)
h = 1 m (distance the block has fallen)
Ws = - (6 kg x 9.8 m/s^2 x 1 m)
Ws = - 58.8 Joules
Therefore, the work done on the cart by the string is -58.8 Joules.