A cord runs around two massless, frictionless pulleys; a canister with mass m=20 kg hangs from one pulley; and you exert a force F if you are to lift the cord.
a) What must be the magnitude of F if you are to lift the canister at a constant speed?
b) To lift the canister by 2 cm, how far must you pull the free end of the cord? During that lift, what is the work done on the canister by c) your force (via the cord) and d) the gravitational force on the canister?
I don't get the picture. What is the second pulley doing?
a) To lift the canister at a constant speed, the force you exert (F) must equal the weight of the canister (mg), where m is the mass of the canister and g is the acceleration due to gravity (approximately 9.8 m/s²). Therefore, F = mg.
b) To lift the canister by 2 cm, we need to find the distance you must pull the free end of the cord.
First, let's assume the cord does not stretch or slip during the lift. In this case, we can use the concept of conservation of rope length. We know that the length of the rope remains constant, so the length of rope pulled should be equal to the distance the canister is lifted.
Thus, to lift the canister by 2 cm, you would need to pull the free end of the cord by 2 cm.
c) During the lift, the work done on the canister by your force (via the cord) can be calculated using the equation: work = force * distance. In this case, the force exerted by pulling the cord is F, and the distance is the 2 cm we pulled the cord. Therefore, the work done by your force is given by work = F * (2 cm).
d) The gravitational force on the canister does not contribute to any work during the vertical lift because the force and the displacement are perpendicular. So, the work done by the gravitational force on the canister is zero.
Note: If there is any vertical displacement in the direction of gravity, the work done by gravity would be calculated as the product of the gravitational force and the vertical displacement. But in this case, the canister is being lifted vertically, so there is no vertical displacement that contributes to the work done by gravity.