Find Time for TBI Injury Risk: Hardwood vs Carpeted Floors

[Snaveekim]

Homework Statement

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, and acceleration less then 800 m/s^2 lasting for any length of time will not cause injury, whereas an acceleration greater then 1000 m/s^2 lasting for a least 1 millisecond will cause injury. suppose a small child rolls off a bed that is 0.40 m above the floor. if the floor is hardwood, the child's head is brought to rest in approximately 2.0 mm. if the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall cound result in a head velocity greater or less than the speed you calculate

Homework Equations

Vf=at+Vo

The Attempt at a Solution

a=-9.8 m/s^2
t=?
Vo=0
Xo=0
Xf=.4m

The only problem I have with this question is, finding time, and without time I couldn't really start. so any tips on how to start this? I don't want the answer really this is my first year of physics and I would love to understand this.
So if someone could teach me how to solve for time that would be great!

 

[PhanthomJay]

You first need to find the speed of the child's head at the instant it hits the floor. You can do this without knowing the time of the fall, by using another kinematic equation. then move on to the 2nd step to calculate the acceleration during , and duration of , the impact.

Welcome to PF!

 

[Snaveekim]

You first need to find the speed of the child's head at the instant it hits the floor. You can do this without knowing the time of the fall, by using another kinematic equation. then move on to the 2nd step to calculate the acceleration during , and duration of , the impact.

Welcome to PF!

I don't know many Equations so would you mind showing me the way?

and thank you and congrats on 4,444 posts :)

 

[PhanthomJay]

Make it 4445

After learning about vectors, you should next learn, understand, and memorize the kinematic motion equations for constant acceleration. See here

http://www.physicsclassroom.com/class/1dkin/u1l6a.cfm

 

[asteriatic]

I would approach this problem by first identifying the key variables and equations needed to solve it. In this case, we have the initial velocity (Vi), final velocity (Vf), acceleration (a), and displacement (d). The equation we can use to solve for time is:

Vf = Vi + at

We can rearrange this equation to solve for time:

t = (Vf - Vi)/a

Now, let's plug in the values given in the problem:

Vi = 0 (since the child starts with zero velocity)
Vf = 0 (since the child comes to rest)
a = -9.8 m/s^2 (since the acceleration due to gravity is acting in the opposite direction of the child's motion)
d = 0.4 m (since the child falls a distance of 0.4 m)

Plugging these values in, we get:

t = (0 - 0)/(-9.8) = 0 seconds

This means that the time of impact for both the hardwood and carpeted floors is 0 seconds. However, we can also calculate the time it takes for the child's head to come to rest after impact by using the equation:

Vf^2 = Vi^2 + 2ad

Again, we know that Vi = 0 and Vf = 0, so we can rearrange the equation to solve for time:

t = (Vf^2 - Vi^2)/2a

Plugging in the values, we get:

t = (0^2 - 0^2)/2(-9.8) = 0 seconds

This means that it takes 0 seconds for the child's head to come to rest after impact on both the hardwood and carpeted floors.

Now, let's calculate the deceleration in each case. We can use the equation:

a = (Vf - Vi)/t

For the hardwood floor, we know that Vi = 0, Vf = 0, and t = 0, so the deceleration is:

a = (0 - 0)/0 = undefined

This means that the deceleration on the hardwood floor is infinite, since the child's head comes to a stop in a very short amount of time.

For the carpeted floor, we know that Vi = 0,