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Old Aug 9th 2019, 07:32 AM   #1
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Kinematics IB question, explanation needed

Could someone please explain (c) and (d) in the question below and attachment. When I tried, I got 735 N, but that isn't the right answer. Thanks in advance for the help.

51 The diagram shows a person in an elevator pulling
on a rope that goes over a pulley and is attached
to the top of the elevator. The mass of the elevator
is 30.0 kg and that of the person is 70 kg.
a On a copy of the diagram, draw the forces on
the person.
b Draw the forces on the elevator.
c The elevator accelerates upwards at 0.50 m s−2.
Find the reaction force on the person from
the elevator fl oor.
d The force the person exerts on the elevator
fl oor is 300 N. Find the acceleration of the
elevator (g = 10 m s−2 ).
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Kinematics IB question, explanation needed-annotation-2019-08-09-200044.png  
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Old Aug 10th 2019, 02:26 PM   #2
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forces on the person;

Tension, T, upward
Normal force of the elevator floor on the person, N, upward
person weight, Mg, downward

forces on the elevator;

Tension, T, upward
Normal force of the person on the elevator floor, N, downward
elevator weight, mg, downward

(c) a = 0.5 m/s^2 upward

T + N - Mg = Ma
T - N - mg = ma
----------------------
2T -(M+m)g = (M+m)a

2T = (M+m)(g+a) = (100 kg)(10.5 m/s^2) = 1050 N

T = 525 N

using the net force equation on the person

N = M(g+a) - T = (70 kg)(10.5 m/s^2) - 525 N = 210 N

(d) N = 300 N

T + N - Mg = Ma
-(T - N - mg = ma)
-----------------------
2N - Mg + mg = Ma - ma

2N - (M-m)g = a(M-m)

[2N - (M-m)g]/(M-m) = a

[600 N - 400 N]/(40 kg) = 5 m/s^2
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