Miquel, mass M=75.0kg, is in an elevator, standing on a spring scale which rests

Question

Miquel, mass M=75.0kg, is in an elevator, standing on a spring scale which rests on the floor of the elevator. when the elevator is at rest, the scale reads his true wight of 750N (taking g=10m/s^2)
Total mass of elevator and contents (including miquel and scale) is MElevator=1000kg. the elevator is supported by a cable that wraps around a pulleey. the cable doesn't slip on the pulley. the pulley is rotated with a large motor.

the vertical velocity of the elevator as a function of time as it goes from ground flour to third floor is the following: accelerates from 0.00m/s to 4.00m/s uniformly in 1.00s, then continues at a rate of 4.00m/s for 2.00s then slowing down uniformly until stop in 1.00s.

How far does the elevator travel in the 4 seconds it takes to go from ground floor to third floor?
A)8m
B)4m
C)16m
D)12m
E)10m

At time 4.5s, when the elevator is at rest @ third floow, what is the tension in the cable just above the elevator?

A)10000N
B)4000N
C)5000N
D)14000N
E)8800N

At t=0.5sm what is the magnitude if the acceleration of the elevator?

A)0m/s^2
B)2m/s^2
C)4m/s^2
D)8m/s^2
E)10m/s^2

@ t=0.5s what is tension in the cable just above the car?

A)10000N
B)4000N
C)5000N
D) 14000N
E)8800N

What is the correct ranking for the scale reading R(t) at t=0.5, 2.0, 3.5, and 4.5s?

A)R(0.5)=R(2.0)=R(3.5)=R(4.5)
B) R(0.5)<R(2.0)=R(3.5)>R(4.5)
C) R(0.5)>R(2.0)=R(3.5)>R(4.5)
D) R(0.5)=R(2.0)>R(3.5)=R(4.5)
E) R(0.5)>R(2.0)=R(3.5)>R(4.5)

What are the units of impule?

A)m/s^2
B)N/s^2
C)Kg/s
D)N*s^2
E)N*s

From t=0 to t=1, what is the magnitude of the net impulse on the elevator (using units chosen in previous question)?

A)0
B)1000
C)2000
D)4000
E)5000

From t=1 to t=2 what is the net work done on the elevator?

A) 0J
B)80000J
C)6000J
D)-80000J
E)-6000J

Shortly after t=4.5s the cable breaks. The elevator is falling and the emergency brake has not been activated yet. What is the scale reading (neglect possible oscillations of the spring of the scale)?

A)750N
B)more than 750N and less than 1500N
C)less than 750N and greater than 0N
D)0N
E)more than 1500N

Explanation / Answer

At t = 0 the elevator isn't moving. At t = 1 it has uniformly sped up to 4 m/s. So the average speed for this one second was 2 m/s. Distance = rate times time D = r*t t = time T = tension 2m = 2m/s*1s in seconds two and three it is going 4 m/s D = r*t = 4 m/s * 2s In the fourth second it slows down to zero again opposite of what happend in the first second, so it went another 2 m. 2m + 8m + 2m = 12m Answer D At t = 4.5 additional acceleration = 0, so just gravity Tension T = mg = 1000kg*10m/s^2 = 10,000 N Answer A At t = 0.5 we are in the uniform acceleration where we increase our speed 4 m/s in one second, this is 4 m/s^2 Answer C At t = 0.5 the T = ma. acceleration = g + 4 m/s^2 since the cable has to not just hold, but accelerate the elevator. T = 1000kg*14m/s^2 = 1400N Answer D Ranking in the first second (0

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