A 3kg mass is resting on a newton balance in an elevator. Complete the table to show the reading on the balance under the conditions of movement of the elevator given.

A) Stationary
B) Moving up at 2.0ms^-1
C)Moving down at 2.0ms^-1
D) Moving up at 2.0ms^2
E) Moving down at 2.0ms^-2

Question

A 3kg mass is resting on a newton balance in an elevator. Complete the table to show the reading on the balance under the conditions of movement of the elevator given.

A) Stationary
B) Moving up at 2.0ms^-1
C)Moving down at 2.0ms^-1
D) Moving up at 2.0ms^2
E) Moving down at 2.0ms^-2

anonymous · Answer

for a-e what would the reading on the newton balance be?

espex · Answer

Well, if you think about the forces that are in play, if the elevator is stationary then there is just the mass pressing against the scale, the scale pressing back. If it is moving up then the scale is pressing against the mass with the normal force plus the force applied by the upward acceleration, if there IS NO acceleration then there is no added force. If the elevator is moving downward then the force the elevator is pushing on the scale with is less and as such the scale is pressing against the mass with less force.

anonymous · Answer

what would the readings on the newtons balance be??

espex · Answer

F=ma, so your readings would be the force (in newtons) equal to the mass times acceleration. So if you are stationary and your mass is 3kg and your acceleration due to gravity is 9.8m/s^2 then you would have a reading of 29.4N
When you are in motion you have the normal force plus the added force due to acceleration, so the sum of forces would be F1 + F2. If you look at the second and third question you should notice that they give you a velocity that is constant. which means there is no acceleration so any potential F2 would be equal to 0.
The fourth and fifth question have you moving up and down respectively, so you will have your initial force plus the force added through acceleration.
Going up you have:$$\sum F=mg+(m(g-a)) \rightarrow (3kg)(9.8\frac{m}{s^2}) + (3kg(9.8\frac{m}{s^2}-2\frac{m}{s^2}))$$ 29.4N+23.4N=52.8N
Your acceleration is a -2 because you are going the opposite direction of gravity but your weight is positive because the force is directed towards the mass and according to Newton's third law, for every action there is an equal and opposite reaction so the mass is pressing back.
Now using the same logic and realizing that when you are going down the acceleration is in the same direction as gravity, but the force is away from the mass, solve the remaining question.