Calculating Final Velocity with Acceleration and Normal Force

In summary, when determining the final velocity of an elevator after 15 seconds of constant acceleration in order for the rider to feel twice as heavy as when at rest, it is important to consider the normal force exerted by the floor. This can be found by using the equation F_g + N = m a, where F_g is the force of gravity, N is the normal force, m is the mass, and a is the acceleration. It is also important to draw a free body diagram and identify all forces involved.
  • #1
oooo
53
0
This is a question I keep getting wrong on my Physics homework:
An elevator is moving with an initial velocity of 10 m/s downward with a 47 kg rider standing inside. What should be the final velocity of the elevator after 15 seconds of constant acceleration if the rider is to feel twice as heavy as he does when at rest? Upward is the positive direction.

Please follow the suggested sequence for arriving at the final velocity.

Step 1: What is the normal force on the rider during the 15-second acceleration period? What I did was: find the acceleration and multiplied that by the mass to get the net force. Then I subtracted the force of gravity from the net force to get the normal force. However there are two problems with my approach : (1) The steps I completed to find the normal force were seen further down the line of steps suggested for finding the final velocity (signifying that I did my process out of order) and (2) The answer was marked incorrect.
Please help, I am very confused. :frown:
 
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  • #2
Confused :P

i thought about it and now I am confused.
Considering the wieght of the perosn is (47)(9.8) = wieght
to get twice the wieght or 2(wieght)= (47)(9.8)(2)
since multiplication is culmative or the order don't matter we can say eithier their mass or 9.8 or gravity has doubled. there mass is probably constant...
so why can't we say the elavator must move up at 9.8m/s in order for their wieght to double that of rest?
 
  • #3
and so if we assume the velocity is 9.8 m/s, where can we go from there to find the normal force?
 
  • #4
God64bit said:
i thought about it and now I am confused.
Considering the wieght of the perosn is (47)(9.8) = wieght
to get twice the wieght or 2(wieght)= (47)(9.8)(2)
since multiplication is culmative or the order don't matter we can say eithier their mass or 9.8 or gravity has doubled. there mass is probably constant...
so why can't we say the elavator must move up at 9.8m/s in order for their wieght to double that of rest?
the fact that he feels twice as heavy does not mean that his weight has changed. The weight is always mg downward. There are two forces acting on the person: the force of gravity downward and the normal force exerted by the floor acting upward. The fact that he feels twice as heavy is due to the fact that the *normal* force exerted by the floor is twice what he usually experiences, so the normal force has a magnitude of 2mg and is acting upward. So you get the equation [itex] (F_g)_y + N_y = m a_y \rightarrow -mg + 2 mg = m a_ y [/itex].
Therefore a_y is + 9.8 m/s^2.

You should always draw a free body diagram and identify clearly the forces. The weight never changes (unless you go to a very high altitude)
 
  • #5
lets leave out everything we have done so far at rest what is Fn?
Fn=mg
so his normal force is (47)(9.8) or 460.6N now "if the rider is to feel twice as heavy as he does when at rest?" if that's how much he feels at rest how does he wieght is that's doubled?
 
  • #6
nrqed said:
the fact that he feels twice as heavy does not mean that his weight has changed. The weight is always mg downward. There are two forces acting on the person: the force of gravity downward and the normal force exerted by the floor acting upward. The fact that he feels twice as heavy is due to the fact that the *normal* force exerted by the floor is twice what he usually experiences, so the normal force has a magnitude of 2mg and is acting upward. So you get the equation [itex] (F_g)_y + N_y = m a_y \rightarrow -mg + 2 mg = m a_ y [/itex].
Therefore a_y is + 9.8 m/s^2.

You should always draw a free body diagram and identify clearly the forces. The weight never changes (unless you go to a very high altitude)

So in english I am wrong and what i said won't work?
 
  • #7
God64bit said:
lets leave out everything we have done so far at rest what is Fn?
Fn=mg
so his normal force is (47)(9.8) or 460.6N now "if the rider is to feel twice as heavy as he does when at rest?" if that's how much he feels at rest how does he wieght is that's doubled?
I am not sure I understand the sentence. But the point is that the weight is actually unchanged. If he *feels* twice as heavy it is because the NORMAL force is twice as large as when there is no acceleration. You are right that the normal force when there is no acceleration is mg (as long as no other force beside gravity is in effect). So if he feels twice as heavy it means that the normal force will be 2mg (but the weight stays the same...mg downward)
 
  • #8
so the normal force is (2)(460.6)?
 
  • #9
oooo said:
so the normal force is (2)(460.6)?
yes. And is acting upward. The weight is the same as always, mg acting downward
 
  • #10
thanks for clearing that up for me!
 
  • #11
a related question: If a block whose mass is 17 kg is attached to a rocket that exerts 169.88 N upward on the block, what is its acceleration?
I thought to just do a=F/m, so a= 169.88/17 where a is roughly 9.993 m/s^2. This is wrong. What is the matter with what I am doing?
 
  • #12
oooo said:
a related question: If a block whose mass is 17 kg is attached to a rocket that exerts 169.88 N upward on the block, what is its acceleration?
I thought to just to a=F/m, so a= 169.88/17 where a is roughly 9.993 m/s^2. This is wrong. What is the matter with what I am doing?

Again, you should be thinking in terms of free body diagrams and thinking about all the forces involved. There is the force exerted by the rocket and there is still the force of gravity acting downward! (the weight if you will). SO the equation is +169.88 - mg = m a_y.
 
  • #13
oh, I understand now, thanks.
 

1. What is the relationship between force and acceleration?

The relationship between force and acceleration is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be, and the greater the mass of the object, the smaller its acceleration will be.

2. How is force measured?

Force is measured in Newtons (N), which is a unit of measurement in the International System of Units (SI). One Newton is equal to the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

3. Can force and acceleration be negative?

Yes, force and acceleration can be negative. Negative force indicates that the force is acting in the opposite direction of the positive reference direction, while negative acceleration indicates that the object is slowing down or accelerating in the opposite direction of the positive reference direction.

4. How does friction affect force and acceleration?

Friction is a force that acts in the opposite direction of an object's motion, and it can decrease the acceleration of an object. This is because friction creates resistance, making it more difficult for an object to move and therefore reducing its acceleration. However, friction can also be beneficial in some cases, such as when it provides necessary traction for objects to move.

5. Can an object have acceleration without a force acting on it?

No, an object cannot have acceleration without a force acting on it. According to Newton's first law of motion, also known as the law of inertia, an object at rest will remain at rest and an object in motion will continue moving at a constant velocity in a straight line unless acted upon by an external force. This means that without a force acting on an object, it will not experience any acceleration.

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