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Here's a question. I don't have any problem getting the answer, or identifying the forces, but I'm having trouble explaining why the scale reads what it does.
A woman of mass 65 kg stands inside an elevator on a bathroom scale calibrated to read in Newtons. Calculate the scale reading in each of the following situations and explain in terms of forces acting on the scale why it reads as it does.
As I work these, it's as if a scale reads only the force pushing up on it, rather than down.
a) elevator stationary
65 * 9.8 = 637
force on the scale:
mg down
mg up
the forces balance and the scale does not move. But with a net force of 0, why does it read 637?
b) elevator accelerating upward at 2.0 m/s^2
65 * 11.8 = 767 N
forces on the scale:
mg = 637 N down
mg + m *2.0 = 767 N up
total forces = 130 N up
so to check, f=ma, 130 = 65 a, a = 2
So why does the scale read 767 N? Does a scale just read the highest force pushing on either the bottom or the top?
c) elevator accelerating downward at 2.0 m/s^2
65 * 7.8 = 507N
Forces on scale
mg down, 637 N
mg - m * 2.0 = 507 N up
d) elevator decending with constant velocity
same as part a
e) elevator in freefall after the cable breaks
0 N
mg = 637 down
mg - m*9.81 = 0 N up
A woman of mass 65 kg stands inside an elevator on a bathroom scale calibrated to read in Newtons. Calculate the scale reading in each of the following situations and explain in terms of forces acting on the scale why it reads as it does.
As I work these, it's as if a scale reads only the force pushing up on it, rather than down.
a) elevator stationary
65 * 9.8 = 637
force on the scale:
mg down
mg up
the forces balance and the scale does not move. But with a net force of 0, why does it read 637?
b) elevator accelerating upward at 2.0 m/s^2
65 * 11.8 = 767 N
forces on the scale:
mg = 637 N down
mg + m *2.0 = 767 N up
total forces = 130 N up
so to check, f=ma, 130 = 65 a, a = 2
So why does the scale read 767 N? Does a scale just read the highest force pushing on either the bottom or the top?
c) elevator accelerating downward at 2.0 m/s^2
65 * 7.8 = 507N
Forces on scale
mg down, 637 N
mg - m * 2.0 = 507 N up
d) elevator decending with constant velocity
same as part a
e) elevator in freefall after the cable breaks
0 N
mg = 637 down
mg - m*9.81 = 0 N up
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