Determine Lift Motion & Sketch Kinematics Profile w/ Newton's Laws

[pikachoo]

A 100g weight resting on a scale took a ride in a lift. From the video clip, determine whether is the lift going up or down based on Newton’s Laws of Motion and sketch the kinematics profile (v-t graph) of the lift carriage.


any idea??

 

[2milehi]

Lift is first at rest then goes down and comes to a stop.

 

[HallsofIvy]

If the lift is accelerating upward, then the scale should register mg (the weight of the object) plus "ma". If it is accelerating downward, it would be mg- ma. Of course, if the lift is going up or down at a constant speed, the scale will not tell you which. It's a bit hard to tell form your attachment but I believe 2milehi is correct.

 

[Jimmy]

1) Elevator at rest: 100g
2) Elevator accelerates downward: less than 100g
3) Elevator reaches constant velocity: 100g
4) Elevator slows (acceleration upward): greater 100g
5) Elevator stops: 100g

 

[pikachoo]

can u guys care to explain me why?? i want to know the theory ._>

 

[cepheid]

can u guys care to explain me why?? i want to know the theory ._>

F = ma. Newton's 2nd law says that the NET vertical force F on this object is equal to its mass times its acceleration. The net vertical force is the SUM of all vertical forces acting (taking their directions into account). In the case of this mass, there are two vertical forces acting on it:

1. The normal force pushing up on it from the surface of the scale: N

2. The force due to gravity pulling down on the mass: mg

Now, the KEY point to understand is that the scale does NOT measure mg. The scale measures N: the contact force between you and it. In other words, the scale measures how hard it is pushing up on you.

I'll choose upward to be the positive direction and downward to be the negative direction. I also choose g = +9.81 N/kg so that the gravitational force is given by -mg. Then the net force (sum of all forces) becomes:

F = N - mg = ma

Case 1 -- not accelerating: ma = 0. Therefore N = mg. Since the mass is not accelerating, the vertical forces on it must be balanced. So the scale just supports it against gravity, pushing up on it with a force equal to mg, no more, no less. Hence, the reading on the scale is mg.

Case 2 -- accelerating upwards: ma > 0. Therefore, N > mg. In order for the acceleration to be upward, there must be a net upward force, which means that the scale must push upward on the mass with a force greater than gravity pulls down on it. Hence, the reading on the scale is greater than mg.

Case 3 -- accelerating downwards: ma < 0. Therefore, N < mg. In order for the acceleration to be downward, there must be a net downward force, which means that the scale must push upward on the mass with a force less than gravity pulls down on it. Hence, the reading on the scale is less than mg.

 

[pikachoo]

Am i right to say the lift is at rest thn it move down and then up again as the mass increased till 11x grams

 

[cepheid]

Am i right to say the lift is at rest thn it move down and then up again as the mass increased till 11x grams

When the reading is the nominal value of 100 g, it doesn't necessarily mean that the object is at rest. It just means that it is *unaccelerated*. It could very well be moving with constant speed in either direction.

Similarly, when the reading increases, it means that the mass is *accelerating* upwards. It doesn't necessarily mean that it is moving upwards. For example, when you are descending in an elevator, at the very end of the motion, as you slow to a stop, you feel heavier because your acceleration is upward, even though your velocity is downward. It's important to understand the difference between velocity and acceleration.

Lastly, it's important to understand the difference between mass and weight. Contrary to what the scale says, the mass of the object never changes. It is always 100 g. What the scale measures is weight: the force with which the object pushes down on the scale. So it is the value of this force (in Newtons) that is increasing and decreasing in this experiment. The scale is just converting the weight in Newtons into a mass in grams by assuming (*incorrectly*) that the object is on Earth and is unaccelerated. If you think that this causes confusion, I agree.

 

[pikachoo]

anyone can tell me how to draw the v-t graph. i think i need to interpret from there ._.