In a particular crash test, an automobile of mass 1295 kg collides with a wall and bounces back off the wall. The x components of the initial and final speeds of the automobile are 25 m/s and 1.5 m/s, respectively.
If the collision lasts for 0.11 s, find the magnitude of the impulse due to the collision.
Answer in units of kg · m/s.
impulse=mass(change velocity)
= mass(25+1.5)
To find the magnitude of the impulse due to the collision, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in its momentum. The formula for impulse is:
Impulse = Change in momentum
The change in momentum can be calculated using the formula:
Change in Momentum = Final Momentum - Initial Momentum
To find the final momentum, we calculate it by multiplying the mass of the automobile by its final velocity:
Final Momentum = mass * Final Velocity
Similarly, to find the initial momentum, we calculate it by multiplying the mass of the automobile by its initial velocity:
Initial Momentum = mass * Initial Velocity
Given:
Mass of the automobile (m) = 1295 kg
Initial velocity (Vi) = 25 m/s
Final velocity (Vf) = 1.5 m/s
Collision time (Δt) = 0.11 s
Now, we can substitute these values into the equations:
Final Momentum = m * Vf
Initial Momentum = m * Vi
Change in Momentum = Final Momentum - Initial Momentum
Finally, to find the magnitude of the impulse, we take the absolute value of the change in momentum:
Impulse = |Change in Momentum|
Let's calculate it step by step:
1. Calculate the final momentum:
Final Momentum = 1295 kg * 1.5 m/s = 1942.5 kg·m/s
2. Calculate the initial momentum:
Initial Momentum = 1295 kg * 25 m/s = 32375 kg·m/s
3. Calculate the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum = 1942.5 kg·m/s - 32375 kg·m/s = -30432.5 kg·m/s
4. Calculate the magnitude of the impulse (absolute value of the change in momentum):
Impulse = |-30432.5 kg·m/s| = 30432.5 kg·m/s
Therefore, the magnitude of the impulse due to the collision is 30432.5 kg·m/s.