What is the force of the floor on her feet?

[x86]

Homework Statement

A 55 kg woman jumps to the floor from a height of 1.5 m.

If her body comes to rest during a time interval of 8.00 * 10^-3 seconds, what is the force of the floor on her feet?

Homework Equations

Unit conversion and
g = 9.8m.s^2 ~ 10 m/s^2

The Attempt at a Solution

The way I understand it, she is at rest, so

Fnet = 0

Fnormal - Fg = 0

Fnormal = Fg = mg = 550 N

This is wrong, and the answer is around 300 N. Why is this?

 

[RobLikesBrunc]

Intuitively, does your result make sense to you?

You just said the answer is mg, so the force on her feet is independent of the height from which she jumps. Tell me--if you jump from a step to the ground, do you think you feel the same force as if jumping out of a skyscraper?

What she's really doing is colliding with the ground. During that time she experiences an average force. Can you figure out what this average force is?

 

[RobLikesBrunc]

Also, are you sure that the answer is 300 N?

 

[x86]

Also, are you sure that the answer is 300 N?

Sorry, 3.8 * 10^4 N

Right, so her impact force would be something like

Fi = ma = m * v / t

v at 8 * 10^-3 would be

Vf = Vi + at = 0 - 9.81m/s^2 * 8 * 10^-3 s = 0.07848 m / s

F = (0.078 m/s / 8*10^-3 s) * 55kg = 0.00053625 N

Which would be wrong, considering it would have to be opposite of this force and this would be too small

I know that F= ma, so her Fg - Fi has to = 0

 

[RobLikesBrunc]

Vf = Vi + at = 0 - 9.81m/s^2 * 8 * 10^-3 s = 0.07848 m / s

Look at this carefully and tell me what you did wrong. Don't blindly use equations; think!

 

[x86]

Look at this carefully and tell me what you did wrong. Don't blindly use equations; think!

Vf = Vi + at = 0 - 9.81m/s^2 * 8 * 10^-3 s = 0.07848 m / s

All of the units cancel out well, to provide me with (m/s). I'm assuming that initial velocity is zero (when she steps off the object, her initial velocity will be zero). This should get me her velocity at time t. I don't see any error, except for the sign of the answer (which would be negative in this case due to gravity, going down)

im going to disregard my old attempt and retry another.

At t = 0.008, she should still be in the air, considering she's in the air for...

d = vi * t - g/2 t^2
d = -4.9m/s^2 * 0.008^2 s ^2

At t = 0.008 seconds, she's still in the air (only fallen -0.3136 millimeters). It seems impossible for her to be at rest, because she's not touching the floor yet

 

[RobLikesBrunc]

Vf = Vi + at = 0 - 9.81m/s^2 * 8 * 10^-3 s = 0.07848 m / s

All of the units cancel out well, to provide me with (m/s). I'm assuming that initial velocity is zero (when she steps off the object, her initial velocity will be zero). This should get me her velocity at time t. I don't see any error.

8.00 * 10^-3 seconds is not the time that she drops for--it's the time period of her collision with the ground (i.e. the time period where the force from ground is still accelerating her up). So her final velocity has nothing to do with 8.00 * 10^-3 seconds.

 

[RobLikesBrunc]

At t = 0.008, she should still be in the air, considering she's in the air for...

d = vi * t - g/2 t^2
d = -4.9m/s^2 * 0.008^2 s ^2

At t = 0.008 seconds, she's still in the air (only fallen -0.3136 millimeters). It seems impossible for her to be at rest, because she's not touching the floor yet

Okay, I see the confusion. The question is poorly worded and assumes familiarity with the type of problem it's asking.

It's really saying "The woman's body comes to rest within 8.00 * 10^-3 seconds after contacting the floor". So, the floor is accelerating her up for 8.00 * 10^-3 seconds AFTER she contacts the floor.

 

[x86]

Okay, so her final velocity is 5.4 m/s [down], and she's in the air for 0.15 seconds.

Thank you for your help and for clearing up the confusion.

(5.4 m/s)/(8.00 * 10^-3 s) * 55 kg = 37 125 Newtons

 

[RobLikesBrunc]

Okay, so her final velocity is 5.4 m/s [down], and she's in the air for 0.15 seconds.

Thanks you for your help and for clearing up the confusion.

(5.4 m/s)/(8.00 * 10^-3 s) * 55 kg = 37 125 Newtons

Correct (you have a rounding error, the velocity rounded should be 5.5 m/s--should get you closer to 3.8 * 10^(4) N).

 

[coconut62]

d = vi * t - g/2 t^2
d = -4.9m/s^2 * 0.008^2 s ^2

At t = 0.008 seconds, she's still in the air (only fallen -0.3136 millimeters). It seems impossible for her to be at rest, because she's not touching the floor yet

This calculation seems plausible. Can someone explain why it's wrong?

 

[RobLikesBrunc]

This calculation seems plausible. Can someone explain why it's wrong?

Because the time he used is a measure of how long it takes the floor to accelerate the woman in the opposite direction once she's impacted the form. It is the duration during which the floor is accelerating her (and, physically, it stems from the impact of the woman deforming the surface of the floor).