Understanding Newton's Laws: Solving for Forces in Elevator Scenarios

[BadlyAddicted]

Homework Statement

I have this problem which is confusing me a lot! my lecturer isn't very good and I really need to understand this by tomorrow because I got a test.

Let's say there is an object of mass 50kg in an elevator. So, from my knowledge, when this lift is at rest or moving with _uniform_ velocity, the object exerts a 500N on the floor of the lift and the floor of the lift exerts a force of 500N on the object.

However, if the lift is accelerating upwards at 2m/s^2, then the objectis also accelerating which implies that there is a resultant force (F=ma=50*2=100N). This 100N is acting upwards, right? So, now I'm supposed to find the force exerted by the lift on the object and the force exerted by the object on the lift ... if i reasoned correctly, these are equal. How come? Wouldn't the lift move with constant velocity if the 100N resultant force was balanced? :|

 

[Bill Foster]

Sum up the forces.

At uniform velocity, what is the acceleration?

(1) v=v_0+at

Rearrange it:

(2) \frac{\Delta{v}}{t}=a

Now that you know what the acceleration on the mass is, you can determine the net force on the block:

(3) F=ma

You can combine equations 2 and 3:

(4) m\frac{\Delta{v}}{t}=ma=F

Net force is also given by the summation of forces acting on the block:

(5) F_{net}=N-mg

Now consider the case where the elevator is accelerating upward...

Equation 5 still applies. But this time there is upward acceleration. Use equation 3 to find that net force. Plug it into equation 5 to find N.