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In a particular crash test, an automobile of mass 1271 kg collides with a wall and bounces back off the wall. The x components of the initial and final speeds of the automobile are 19 m/s and 3.3 m/s, respectively. If the collision lasts for 0.16 s, find the magnitude of the impulse due to the collision. Calculate the magnitude of the average force exerted on the automobile during the collision.

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Answer:

28343.3 kgm/s

177145.625 N

Explanation:

u = Initial velocity = 19 m/s

v = Final velocity = -3.3 m/s (opposite direction)

m = Mass of car = 1271 kg

t = Time taken = 0.16 s

Impulse is given by

[tex]J=m(v-u)\\\Rightarrow J=1271(-3.3-19)\\\Rightarrow J=-28343.3\ kgm/s[/tex]

The magnitude of the impulse due to the collision is 28343.3 kgm/s

Force given by

[tex]F=\dfrac{J}{t}\\\Rightarrow F=\dfrac{-28343.3}{0.16}\\\Rightarrow F=-177145.625\ N[/tex]

The magnitude of the average force exerted on the automobile is 177145.625 N

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