11. A car with mass of 1000-kg (mass of the driver included) moving to the right
ID: 1514652 • Letter: 1
Question
11. A car with mass of 1000-kg (mass of the driver included) moving to the right at 20 m/s collides with rear of a 2000-kg truck moving right at 5 m/s. The bumpers lock during the collision. The driver of the car has a mass of 100 kg and his velocity change is the same as that of the car. The collision last for 0.10 s. (a) Calculate the force exerted on the car. (b) Calculate the force exerted on the truck. (c) Calculate the force exerted on the driver. [Answer: (a) -100,000 N; (b) 100,000 N; (c) -10,000 N]
Explanation / Answer
Given data
mass of the car m1 = 1000 kg
velocity of the car u1= 20 m/s
mass of the driver = 100 kg
collision time t = 0.10 sec
mass of the truck = m2 = 2000 kg
velocity of the truck u2 = 5 m/s
From the conservation of linear momentum
initial momentum= final momentum
m1u1 +m2u2 = (m1+m2)*V
where V = final velocity
1000*20 + 2000*5 = 3000*V
V =10 m/s
from Newtons third law
Force exerted on the truck = - force exerted on the car----------------------------(1)
from newtons second law
F(on truck) =mass* acceleration
= ma
=mV/t
=2000*10/0.10= 100000 N
from (1)
force exerted on the car = -100000
Force exerted on the driver
F = mass * acceleration
F = -mV/t
as the driver has the same velocity of the car
F = -100*10/0.10
F(on driver) = -10000 N
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