Trying to solve an elevator problem

[Robertoalva]

Homework Statement

An elevator accelerates downward at 3.2 m/s2. What force does the floor of the elevator exert on a 46 kg passenger?

Homework Equations

T+F=ma
T being tension

The Attempt at a Solution

I don't know if the tension of the elevator line is 9.81N, and in the passenger I got 147.2 N for his force(using the acceleration of the elevator.

 

[ap123]

You don't need the tension of the elevator cable here since it doesn't directly act on the passenger.

Draw a free-body diagram for the passenger and use Newton 2.

 

[Robertoalva]

so i basically get the force of the person by, multiplying 49kg*3.2m/s^2 right? if so, then how do I get the force of the floor? it is less because the elevator is going down right?

 

[ap123]

What are the 2 forces acting on the passenger?
Draw these on a diagram and add them.
Their sum will be the quantity you calculated.
( Make sure that your signs are correct here ).

You are right in saying that the normal force will get less.

 

[Robertoalva]

so, the answer would be 137.39N ? because of the substraction of the normal force of the man and the default force 9.81N?

 

[ap123]

No.

The normal force on the passenger acts upwards, and the weight acts downwards.
The sum of these is the quantity you calculated in #3, ( from F(net) = ma ).

You can work out the normal force from this.
Choose one direction as positive ( eg the downward direction ) and make sure your signs are correct.

 

[Robertoalva]

so it would be 304.06 - 147.2 = 156.86N

 

[ap123]

Where does the 304.06 come from?

You should have something like
mg - n = ma

 

[Robertoalva]

well, is (9.81-3.2)*46= 304.06 and that's the final answer.

 

[ap123]

Yes :)