Question

In a crash test, a 2000-kg van collides with a concrete support. The stopping time interval for the collision is 0.10 s, and the impulse exerted by the support on the van is 5.5×103 N⋅s.

A. Determine the magnitude of the change in momentum.

B. Determine the magnitude of the average force exerted by the concrete support on the van.

C.If the van is constructed to collapse more during the collision so that the time interval during which the impulse is exerted is tripled, what is the magnitude of the average force exerted by the concrete support on the van?

Answer 1

Answer:

(a). The magnitude of the change in momentum is $5.5\times10^{3}\ N.s$

(b). The magnitude of the average force exerted by the concrete support on the van is $5.5\times10^{4}\ N$.

(c). The average force exerted by the concrete support on the van is $1.83\times10^{4}\ N$

Explanation:

Given that,

Mass of van = 2000 kg

Time = 0.10 s

Impulse $J= 5.5 10^{3}\ N.s$

(a). We need to calculate the magnitude of the change in momentum

Using impulse-momentum theorem

Change in momentum = impulse

$J=\Delta p$

Put the value into the formula

$\Delta p= 5.5\times10^{3}\ N.s$

The magnitude of the change in momentum is $5.5\times10^{3}\ N.s$

(b). We need to calculate the magnitude of the average force exerted by the concrete support on the van.

Using formula of impulse

$J=F\times t$

$F=\dfrac{J}{t}$

Put the value into the formula

$F=\dfrac{5.5 10^{3}}{0.10}$

$F=5.5\times10^{4}\ N$

The magnitude of the average force exerted by the concrete support on the van is $5.5\times10^{4}\ N$.

(c). If the impulse is tripled

As time interval is tripled then average force is reduced one third.

We need to calculate the average force exerted by the concrete support on the van

Using formula of impulse

$J=F\times t$

$F=\dfrac{J}{t}$

Put the value into the formula

$F=\dfrac{5.5\times10^{3}}{3\times0.10}$

$F=18333.33\ N$

$F=1.83\times10^{4}\ N$

The average force exerted by the concrete support on the van is $1.83\times10^{4}\ N$

Hence, (a). The magnitude of the change in momentum is $5.5\times10^{3}\ N.s$

(b). The magnitude of the average force exerted by the concrete support on the van is $5.5\times10^{4}\ N$.

(c). The average force exerted by the concrete support on the van is $1.83\times10^{4}\ N$