Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip’s speed at impact is about 2.0 m/s . If this can be reduced to 1.3 m/s or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads.

A)If a typical pad is 5.0 cm thick and compresses by 2.2 cm during the impact of a fall, what acceleration (in m/s2 ) does the hip undergo to reduce its speed to 1.3 m/s ?

B)What acceleration (in g 's ) does the hip undergo to reduce its speed to 1.3 m/s ?

C)The acceleration you found in part A may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts.

Respuesta :

Answer:

(a).The acceleration is 52.5 m/s²

(b). The acceleration is 5.35 g.

(c). The time is 0.038 sec.

Explanation:

Given that,

Initial speed = 2.0  m/s

Distance = 2.2 cm

Final speed = 1.3 m/s

We need to calculate the acceleration

Using equation of motion

[tex]v^2=u^2+2as[/tex]

[tex]a=\dfrac{v^2-u^2}{2s}[/tex]

Put the value into the formula

[tex]a=\dfrac{(1.3)^2-(2.0)^2}{2\times2.2\times10^{-2}}[/tex]

[tex]a=-52.5\ m/s^2[/tex]

Negative sign shows the deceleration

(b). We need to calculate the acceleration in terms g

[tex]a=\dfrac{52.5}{9.8}[/tex]

[tex]a=5.35\ g[/tex]

The acceleration is 5.35 g.

(c). We need to calculate the time

Using equation of motion

[tex]v=u+at[/tex]

[tex]t=\dfrac{v-u}{a}[/tex]

Put the value into the formula

[tex]t=\dfrac{0-2}{-52.5}[/tex]

[tex]t=0.038\ sec[/tex]

Hence, (a).The acceleration is 52.5 m/s²

(b). The acceleration is 5.35 g.

(c). The time is 0.038 sec.

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