A 14,245N auto with a velocity of 6.0m/s crashes into a brick wall. If the car moves 64.0 cm before coming to a stop, what average force does the car exert on the wall?
To find the average force exerted by the car on the wall, we need to use the equation:
Average force = Change in momentum / Time
In this case, the momentum of the car before the collision is given by the product of its mass and velocity:
Momentum before collision = Mass x Velocity
We can rearrange this equation to solve for the mass:
Mass = Momentum before collision / Velocity
Given that the force applied by the car is the same as the force exerted on the wall, we can equate the impulse experienced by the car to the product of the average force and the time:
Impulse = Average force x Time
The impulse experienced by the car is equal to the change in momentum, which we calculate by subtracting the initial momentum from the final momentum:
Impulse = Change in momentum = Momentum after collision - Momentum before collision
Since the car comes to a stop, its final momentum is zero:
Impulse = -Momentum before collision
Now, let's plug in the given values into the equations and solve step by step:
1. Calculate the mass of the car:
Given velocity = 6.0 m/s
Given momentum before collision = Mass x Velocity
Mass = Momentum before collision / Velocity
2. Calculate the momentum before the collision:
Momentum before collision = Mass x Velocity
3. Calculate the impulse experienced by the car:
Impulse = -Momentum before collision
4. Calculate the average force exerted on the wall:
Average force = Impulse / Time
Let's now calculate the values step by step.
Given information:
Velocity of the car (v) = 6.0 m/s
Distance traveled (d) = 64.0 cm = 0.64 m
Force exerted by the car (F) = ?
Step 1: Calculate the mass of the car
Mass = Momentum before collision / Velocity
Since the momentum is equal to the force multiplied by the time (Impulse = Force * Time), we can re-arrange and solve for mass:
Mass = Impulse / (Velocity * Time)
Mass = (Force * Time) / (Velocity * Time)
Mass = Force / Velocity
Step 2: Calculate the momentum before the collision
Momentum before collision = Mass x Velocity
Momentum before collision = (Force / Velocity) * Velocity
Momentum before collision = Force
Step 3: Calculate the impulse experienced by the car
Impulse = -Momentum before collision
Impulse = -Force
Step 4: Calculate the average force exerted on the wall
Average force = Impulse / Time
Average force = (-Force) / Time
Average force = -Force / Time
Based on the given values and calculations, we can conclude that the average force exerted by the car on the wall is equal in magnitude but opposite in direction to the force experienced by the car, which can be calculated using the above equations.