An RV of mass 4000 kg traveling at 30 m s^-1 to the East is struck by a truck of

Question

An RV of mass 4000 kg traveling at 30 m s^-1 to the East is struck by a truck of mass 5000 kg moving at 10 m s^-1 to the North. The vehicles lock together. a. At what speed do they move immediately after the collision? In what direction? b. What is the change in momentum of the RV? Of the truck? c. If the collision takes 0.1 second, what is the magnitude of the average force exerted on the RV by the truck? What is the magnitude of the average force exerted on the truck by the RV? d. What is the total kinetic energy of the vehicles before the collision? After the collision? Is the collision elastic?

Explanation / Answer

Here,

mass of RV , m1 = 4000 Kg

mass of truck , m2 = 5000 Kg

u1 = 30 i m/s

u2 = 10 j m/s

a)

let the final velocity is v

using conseravtion of momentum

m1 * v1 + m2 * v2 = (m1 + m2) * v

4000 * 30 i + 5000 * 10 j = (4000 + 5000) * v

v = 13.33 i + 5.56 j

v = sqrt(13.33^2 + 5.56^2) at arctan(5.56/13.33) degree north of east

v = 14.44 m/s at 22.7 degree north of east

the speed after the collision is 14.44 m/s at 22.7 degree north of east.

b)

change in momentum of RV = 4000 * (30 i - (13.33 i + 5.56 j ))

change in momentum of RV = 4000 *(16.7 i - 5.56 j)

change in momentum of RV = 7.04 *10^4 Kg.m/s

the change in momentum of RV is 7.04 *10^4 Kg.m/s

change in momentum of truck = 7.04 *10^4 Kg.m/s

c)

time , t = 0.1 s

average force exeted on the RV by truck = change in momentum/time

average force exeted on the RV by truck = 7.04 *10^4/.1 N

average force exeted on the RV by truck = 7.04 *10^5 N

the average force exeted on the RV by truck is 7.04 *10^5 N

the force is same for both

the average force exerted on the truck by RV is 7.04 *10^5 N

d)

Total energy before collision = 0.5 * 4000 * 30^2 + 0.5 * 5000 * 10^2

Total energy before collision = 2050000 J

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after the collision

Total energy after the collision = 0.5 * (4000 + 5000) * 14.44^2

Total energy after the collision = 938311.2 J

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