two cars weighing 1500 kg are made to collide with a wall.the initial and final velocities are 15 m/s and 2.6 m/s.if the collision last for 0.15 seconds,then find impulsive force exerted on the car
To find the impulsive force exerted on the car, we can use the principle of impulse and momentum.
Impulse is defined as the change in momentum of an object, and it can be calculated by multiplying the average force exerted on an object over a period of time by the duration of the force. In this case, the force exerted on the car can be determined by calculating the change in momentum and dividing it by the duration of the collision.
Here's the step-by-step process to calculate the impulsive force:
Step 1: Calculate the initial momentum (p1) of the car.
The initial momentum can be calculated using the formula: p1 = mass x initial velocity.
Given that the mass of each car is 1500 kg and the initial velocity is 15 m/s, the initial momentum (p1) is:
p1 = 1500 kg x 15 m/s = 22500 kg·m/s.
Step 2: Calculate the final momentum (p2) of the car.
The final momentum can be calculated using the formula: p2 = mass x final velocity.
Given that the mass of each car is 1500 kg and the final velocity is 2.6 m/s, the final momentum (p2) is:
p2 = 1500 kg x 2.6 m/s = 3900 kg·m/s.
Step 3: Calculate the change in momentum (∆p) by subtracting the initial momentum from the final momentum.
∆p = p2 - p1 = 3900 kg·m/s - 22500 kg·m/s = -18600 kg·m/s (Note: The negative sign indicates a decrease in momentum.)
Step 4: Calculate the impulsive force (F) by dividing the change in momentum (∆p) by the duration of the collision (t).
F = ∆p / t
Given that the duration of the collision is 0.15 seconds, the impulsive force (F) is:
F = -18600 kg·m/s / 0.15 s = -124000 N.
The impulsive force exerted on each car is approximately -124,000 Newtons. The negative sign indicates that the force is in the opposite direction to the initial motion of the cars.