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Please answer each question and tell me whether it is right and show me how to do it and your work.

1. A 250.0g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2/5 N/cm. The block becomes attached to the spring and compresses the spring 12.0cm before temporarily stopping. While the spring is being compressed, what work is done on the block by...

a) the gravitational force on it?

my answer)

-> Work (gravitational) = F * d = (m*g)*h 0.25*9.8*0.12 = 0.29J (my question is that should the work have a negative value because the gravitational foce done on the block is downward?)

b) the spring force on it?

my answer)

-> Work (spring) = 1/2(K*X^) = 1/2*250*0.12^ = -1.8J (What should the sign of the final value(1.8J) be? positive? negative?)

c) What is the speed of the block just before it hits the spring? (Assume negligible friction and air resistance)

my answer)

-> W(gravitational) = delta K (change in kinetic energy) = 1/2(0.25)(vm/s)^2 - 1/2(0.25)(0m/s)^2

v = 1.52 m/s

d) If the speed at impact is doubled, what is the maximum compression of the spring?

my answer)

-> W(spring) - W(gravitational) = delta K (change in kinetic energy)

That is all I could think of. I don't know how else to try this question. I have a test tomorrow, and it will be on this kind of questions. Please help me...

2. A fully loaded, slow-moving freight elevator has a cab with a total mass of 1200.0kg, which is required to travel upward 54.0m in 3.0minutes, starting and ending at rest. The elevator's counterweight has a mass of only 950.0kg, so the elevator motor must help pull the cab upward.

a) What is the total work done by all forces on the elevator - counterweight system?

my answer)

-> Work = delta K (change in kinetic energy) = 1/2(1200kg)(final velocity)^2 = 1/2(1200kg)(om/s) = 600(final velocity)^2 - 0

(final velocity) = 54m / 3min = 0.3m/sec

Work = 600kg(0.3)^2 = 54J (so I got total work equals 54J. But the question asks for the total work done by all forces on the elevator and counterweight system. I don't understand how to find counterweight system. Does my answer include everything that the question asks for? or what should I do?)

b) What is the work done by the motor on the system?

my answer)

-> I really can't do this problem until I finish the part(a). But my idea is that I should subtract the gravitational work from the work of the system. Am I right? If so, I just do mgh(cos180) to find the value of gravitational work. Right?)Please answer each question and tell me whether it is right and show me how to do it and your work.