Question

The largest acceleration that a human has ever endured occurred when a race car accidentally crashed into a wall. The car was traveling at a speed of 172.8 km/h when it hit the wall. The car came to a complete stop 2.72 ´ 10–2 s later.

a. Calculate the acceleration of the car using the acceleration formula. Express your answer in both m/s2 and in “g’s.” One g is equal to the free-fall acceleration of 9.8 m/s2.







b. Suppose the driver of the car had a mass of 70.0 kg. What was the unbalanced force on his body as the car underwent negative acceleration?

Answer 1

(a) The acceleration oF the car is
`-1764.7 m/s^2` or -180.1 g’s.

(b) The magnitude of the force on the driver's body is 123529 Newtons

Step-by-step explanation:

Given that:

The initial velocity of the car before the impact, u=172.8 km/h

Or,
`u =172.8 * \frac {1000}{3600} m/s= 48m/s`

As the car came to a complete stop after the collision, so the final velocity of the car, v=0.

The time required to stop the car completely,
`t=2.72* 10^(-2) s`

(a) Assuming the acceleration is constant, so

Acceleration,
`a= (v-u)/t`

So,
`a=\frac {0-48}{2.72* 10^(-2)}=-1764.7 m/s^2`

Now, expressing the acceleration in the unit od "g's",

`a=-1764.7* (g)/(g) \\\\\Rightarrow a=-1764.7 \;m/s^2* (g)/(9.8\; m/s^2) \\\\\Rightarrow a=-180.1 g`

Hence, the acceleration od the car is -1764.7
`m/s^2` or -180.1 g’s.

(b) Mass of the driver of the car, m=70.0 kg

The acceleration of the body of the driver is the same as the acceleration of the car.

So, the acceleration faced by the driver,
`a= -1764.7 m/s^2`

As forec = mass x acceleration, so

The force on the driver's body = 70 x (-1764.7)= -123529 Newtons.

The negative sign means the force is in the opposite direction of the direction of motion of the car.

Hence, the magnitude of the force on the driver's body is 123529 Newtons