The figures show loads hanging from the ceiling of an elevator that is moving at

Question

The figures show loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load, given that

1 = 40.0°,

2 = 50.0°,

3 = 65.0°,

m1 = 7.00 kg,

and

m2 = 11.0 kg.

The figure below shows the speed of a person's body as he does a chin-up. Assume the motion is vertical and the mass of the person's body is 56.2 kg. Determine the force exerted by the chin-up bar on his body at the following times.

(a)    t = 0
N

(b)    t = 0.5 s
N

(c)    t = 1.1 s
N

(d)    t = 1.6 s.
N

Explanation / Answer

a )

using vertical components

T1 sin40 + T2 sin50 = m1 g

T1 X 0.642 + T2 X 0.766 = 7 X 9.8

0.642T1 + 0.766 T2 = 68.6 --------------- 1

using horizontal components

T1 cos40 = T2 cos50

T1 X 0.766 = T2 X 0.642

0.642T2 = 0.766 T1  

T2 = 1.19 T1 --------------- 2

from 1 and 2

0.642T1 + 0.766 (1.19 T1) = 68.6

T1 = 68.6 / 1.553

T1 = 44.17 N

and

T2 = 1.19 T1

T2 = 1.19 X 44.17

T2 = 52.56 N

T3 = m1 g

T3 = 7 X 9.8

T3 = 68.6 N

b )

using vertical components

T1 X sin65 = m2 g

T1 = 11 X 9.8 / sin65

T1 = 118.94 N

using horizontal components

T2 = T1 cos65

T2 = 50.266N

T3 = m2 g

T3 = 11 X 9.8

T3 = 107.8 N

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