A large truck with a mass of 6500·kg and going 20·m/s east collides with a car whose mass is 1100·kg and which is at rest. If the impulse exerted on the car by the truck is 12000·N·s east, find the impulse exerted by the car on the truck. Take east as the postive direction
To find the impulse exerted by the car on the truck, we need to use the principle of conservation of momentum. In a collision, the total momentum of the system remains constant before and after the collision.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is represented as:
p = m * v
Where:
p = Momentum
m = Mass
v = Velocity
Before the collision, the truck has a mass of 6500 kg and is moving at a velocity of 20 m/s east. The car has a mass of 1100 kg and is initially at rest. The momentum of the truck-car system before the collision can be calculated as follows:
Initial momentum of the truck-car system = (Mass of Truck * Velocity of Truck) + (Mass of Car * Velocity of Car)
= (6500 kg * 20 m/s) + (1100 kg * 0 m/s)
Now, let's calculate the initial momentum of the truck-car system:
Initial momentum of the truck-car system = (6500 kg * 20 m/s) + (1100 kg * 0 m/s)
= 130,000 kg·m/s
After the collision, the truck-car system will have a new momentum. Since the total momentum is conserved, we can use the impulse-momentum principle to determine the new momentum:
Impulse = Change in Momentum
Given that the impulse exerted on the car by the truck is 12000 N·s east, we can set up the equation as follows:
Impulse exerted by the truck on the car = Change in momentum of the car
= Final momentum of the car - Initial momentum of the car
The final momentum of the car can be calculated as:
Final momentum of the car = Initial momentum of the car + Impulse exerted by the truck on the car
Substituting the values into the equation:
Final momentum of the car = 0 + 12000 kg·m/s
Since the total momentum is conserved, the final momentum of the truck-car system is equal to the final momentum of the car. Therefore, the final momentum of the truck-car system after the collision is:
Final momentum of the truck-car system = Final momentum of the car
= 12000 kg·m/s
Now, we can find the impulse exerted by the car on the truck by applying the impulse-momentum principle. Since we are assuming east as the positive direction, the impulse exerted by the car on the truck will also be east. The impulse-momentum principle states that the impulse is equal to the change in momentum. Mathematically:
Impulse exerted by the car on the truck = Final momentum of the truck - Initial momentum of the truck
Substituting the values into the equation:
Impulse exerted by the car on the truck = (Final momentum of the truck - Initial momentum of the truck)
Impulse exerted by the car on the truck = (12000 kg·m/s) - (130,000 kg·m/s)
= -118,000 kg·m/s (east)
Therefore, the impulse exerted by the car on the truck is -118,000 kg·m/s (east).