A car is stationary at a stop sign when it is hit directly from behind by a truck of mass 3000kg which was travelling at a speed of 9 m/s immediately before the collision. The two vehicles lock together and move forward with an initial speed of 6 m/s.
a) what is the mass of the car?
b) If the car had been designed with a crumple zone, explain in correct physics term, why this might reduce the risk of injury to the driver.
initial momentum = 3000*9
final momentum = (3000+m)*6
final momentum = initial momentum
solve for m
b) F = m a
If a is less force is less.
a is rate of change of velocity
if velocity change is spread out over a longer time, a is less and F is less.
To solve these problems, we can use the principles of conservation of momentum and kinetic energy.
a) To find the mass of the car, we can use the conservation of momentum principle.
The momentum before the collision is equal to the momentum after the collision, since there are no external forces acting on the system.
The momentum before the collision is given by:
Initial momentum of truck = mass of truck * velocity of truck
Initial momentum of truck = 3000 kg * 9 m/s
The momentum after the collision is given by:
Final momentum of combined vehicles = (mass of car + mass of truck) * velocity after the collision
Final momentum of combined vehicles = (mass of car + 3000 kg) * 6 m/s
Since the two momenta are equal, we can set up an equation to solve for the mass of the car:
3000 kg * 9 m/s = (mass of car + 3000 kg) * 6 m/s
Simplifying the equation:
27000 kg*m/s = 6 m/s * mass of car + 18000 kg*m/s
Subtracting 18000 kg*m/s from both sides:
9000 kg*m/s = 6 m/s * mass of car
Dividing both sides by 6 m/s:
1500 kg = mass of car
Therefore, the mass of the car is 1500 kg.
b) A crumple zone is a part of the car designed to absorb and dissipate the kinetic energy during a collision. When a collision occurs, the crumple zone deforms, absorbing and distributing the energy over a longer period of time. This reduces the impact force exerted on the occupants of the car and decreases the risk of injury.
In physics terms, the crumple zone increases the collision time (the duration of the impact) during a crash. According to the impulse-momentum principle, the change in momentum is directly proportional to the impulse applied to an object, and the impulse is related to the force and the collision time. By increasing the collision time, the force exerted on the occupants decreases, reducing the risk of injury. Additionally, the crumple zone also helps in redirecting some of the impact force away from the passenger compartment, providing a safer environment for the driver.