(a) An elevator of mass m moving upward has two forces acting on it: the upward

Question

(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? Both forces are equal. (b) When the elevator is moving at a constant velocity upward, which is greater, T or w? Both forces are equal. (c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w? Both forces are equal. (d) Let the elevator have a mass of 1300 kg and an upward acceleration of 2.1 m/s2. Find T. N Is your answer consistent with the answer to part (a)? Yes O N (e) The elevator of part (d) now moves with constant upward velocity of 10 m/s. Find T. N Is your answer consistent with your answer to part (b)? Yes No (f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.30 m/s2. Find T N Is your answer consistent with your answer to part (c)? Yes No

Explanation / Answer

a) when the elevator is accelerating upward then net force on it : ( w= weight = mg)

ma= T- mg ----------------------------1

in this case : T is greater.

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b) when it is moving with a constant velocity ie a= 0, from eq 1:

0= T- mg

T= mg

so both forces are equal.

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c) when elevator is upward but accelerating downward then net force will be in downward direction so w (= mg) is greater.

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d) m= mass= 1300 kg

a= acceleration = 2.1 m/s2

from eq 1:

ma= T - mg

T= m(a+g)

T= 1300*( 2.1+ 9.8)

T= 15470 N

and weight , w= mg = 1300*9.8 = 12740 N

since T> w so ans is consistent with part a.

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