Question

(13.1) An elevator riding in a frictionless vertical shaft has total mass of 1000 kg.

(a) The elevator cable exerts a force of 9000 N in the upward direction on the elevator. Determine (i) the acceleration of the elevator, and (ii) how long it takes for the elevator, starting from rest, to attain a speed of 5 m/s.

(b) The cable exerts a force of 12000 N [up] on the elevator. Determine (i) the acceleration of the elevator, and (ii) how long it takes for it to attain a speed of 5 m/s, starting from rest.

(13.2) A block of mass M = 5 kg is at the origin of a horizontal frictionless plane. At the instant t = 0, it is moving in the negative x-direction with speed 4 m/s. A constant force of 10 N is applied to the block in the positive x-direction starting at t = 0 and lasting until a later time, tf , when the block comes to rest.

(a) Draw a free body diagram and enumerate the forces which act on the block.

(b) Compute the acceleration of the block while the force is applied.

(c) Compute the (i) time, tf , and (ii) position, xf , at which the block stops.

Answer 1

13.1

a)

i)

T = m ( g + a)

9000 = 1000 ( 9.8 + a)

a = - 0.8 m/s^2

negative sign indicates that elvator moving downward direction

ii)

time at which

t = v/ a = 5 / 0.8 = 6.25 s

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b)

i)

12000 = 1000(9.8 + a)

a = 2.2 m/s^2

ii)

t = 5 / 2.2 = 2.273 s

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plz post other problem separately

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