A 100kg person stands on a scale?

Question

a.) What would be the scale readout? ___ N

(How does this compare with the person's weight?)

b.) If the person stands on the scale in an elevator accelerating upwards at 5 m/s2, what is the scale readout?

____N

(How does this compare with the person's weight?)

c.) If the person stands on the scale in an elevator accelerating downwards at 5 m/s2, what is the scale readout?

___N

(How does this compare with the person's weight?)

d.) If the person stands on the scale in an elevator accelerating downwards at 9.8 m/s2, what is the scale readout?

___N

(How does this compare with the person's weight?)

e.) Explain why your result from part d makes sense. Is the actual weight of the person any different? What does the person perceive his weight to be?

f.) If the person stands on the scale in an elevator moving up at a constant speed of 100 m/s, what is the scale readout?

___N

(How does this compare with the person's weight?)

Answer 1

I'll not do your homework, but I'll give you some hints:

a 100kg person stands on a scale?

a.) What would be the scale readout? ___ N

(How does this compare with the person's weight?)

w = W - C = mg - mw^2r; where m = 100 kg, g = 9.81 m/sec^2, w = 2pi rad/24 hours [you need to change this to rad/sec], and r = R cos(L) Earth's radius of rotation at a given latitude L and the radius of Earth R.  w is the net weight you are looking for, it's what you will read on the scale.  In most daily problems, we can ignore centrifugal force C and set it to C = 0.  If C = 0, the w = W = mg, which is the weight in Newtons.

b.) If the person stands on the scale in an elevator accelerating upwards at 5 m/s2, what is the scale readout?

____N

(How does this compare with the person's weight?)

w = W + ma = mg + ma = m(g + a); where a = 5 m/sec^2.  Is the net weight w greater or lesser than W?

c.) If the person stands on the scale in an elevator accelerating downwards at 5 m/s2, what is the scale readout?

___N

(How does this compare with the person's weight?)

w = W - ma = m(g - a); again is w > W or < W in this case?

d.) If the person stands on the scale in an elevator accelerating downwards at 9.8 m/s2, what is the scale readout?

___N

(How does this compare with the person's weight?)

w = W - ma; where a = 9.8 m/sec^2 ~ g = 9.81 m/sec^2; so what's w now?  Is w >, <, or = W?  Maybe w ~ 0, how's that compare to W?

e.) Explain why your result from part d makes sense. Is the actual weight of the person any different? What does the person perceive his weight to be?

If the person is accelerating downward at the same rate that gravity pulls downward how would she feel...lighter, heavier, same?  Think about your own experience in an elevator; when it suddently lurches downward, did you feel lighter, heavier, or the same for a moment?  Check the signs on the second term in the equations for w.  What do they mean as far as that person's experience.

f.) If the person stands on the scale in an elevator moving up at a constant speed of 100 m/s, what is the scale readout?

___N

(How does this compare with the person's weight?)

w = W + ma; when v = constant velocity = 100 mps, what's the value of a?  Does the second term (ma) add or subtract value to or from W?