Can someone help me understand the apparent weight of a body on a moving lift?

[shreyasshree]

The book says:

The lift is at rest---> weight=mg

The lift is moving up or down with uniform velocity---> weight=mg

I understood this far.

Now, it says that when the lift is accelerating uniformly

a)upwards--->weight=m(g+a)

b)downwards--->weight=m(g-a)

My problem is: Why is it + in a) and - in b)?

 

Thnx

[imatfaal]

Draw a diagram (always but always draw a diagram) and label all forces. Getting which force is weight correct will go a long way to answering your question. Remember that forces and accelerations are vectors and have direction.

 

and

 

Moved to homework help.

[Greg H.]

The first thing to understand is that from the frame of reference of the person in the lift, there is no difference between the acceleration of the lift and gravity - both are accelerations.

 

The second thing to keep in mind is that acceleration (including gravity) is a vector. The signs change because the direction component of that vector changed.

[studiot]

I have to say that if I was just struggling to puzzle out what was meant by the book, I would find the explanations less than helpful.

 

First is to know what is meant by 'apparent weight'.

 

This is the reading that would be obtained by standing the object on a spring type scale.

 

It is the force that the object exerts on the scale.

 

Now Newton's third law tells us that the floor of the lift or the scale pan exerts an upward force on the object and the object exerts a downward force on the scale pan.

 

Whichever way the lift is moving the object always exerts a downward force, due to gravity.

 

When the lift is accelerating upwards, the lift exerts an additional upwards force on the object due to its acceleration (ie in order to accelerate the object upwards).

 

Consequently the object exerts an additional downward force on the lift by Newton's third law. That is it presses harder on the floor when the lift is accelerating upwards.

 

So for upwards acceleration your book is saying that you add the gravitational force on the object to the reaction force due to the acceleration.

 

Does this help?

[shreyasshree]

The first thing to understand is that from the frame of reference of the person in the lift, there is no difference between the acceleration of the lift and gravity - both are accelerations.

 

The second thing to keep in mind is that acceleration (including gravity) is a vector. The signs change because the direction component of that vector changed.

Yeah ! I got it today! Thnx. Conformed that what i thought was kind of right!