Question

A 50 kg vehicle has 10,000 J of Kinetic Energy and runs into a wall, coming to a complete stop in 0.3 seconds. What is the force of the impact?

Option 1: 166,666.67 N
Option 2: 150,000 N
Option 3: 200,000 N
Option 4: 100,000 N

Answer 1

To find the force of the impact when the vehicle hits the wall, we would use the work-energy principle and the impulse-momentum theorem. The vehicle's initial velocity is required to accurately calculate the force, which is not provided in the options given. Without the initial velocity, we cannot correctly choose from the given options.

Step-by-step explanation:

To calculate the force of the impact when a 50 kg vehicle which has 10,000 J of kinetic energy hits a wall, we start by using the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy. Since the vehicle comes to a stop, the kinetic energy goes to zero, meaning the work done on the vehicle is equal to the initial kinetic energy of the vehicle. We can express this as:

Work = Force x Distance

Here, the work done is 10,000 J. If we assume the impact brings the car to a stop over a very short distance (essentially reaching zero), the distance factor is practically negligible and the main concern is the time over which the force acts. Now, impulse is given by the product of the force and the time it is applied, which also equals the change in momentum.

Impulse = Force x Time = Change in momentum

Since the final velocity is zero and the initial momentum is given by (mass x initial velocity), we can set the impulse equal to the initial kinetic energy divided by the initial velocity of the vehicle. However, the initial velocity is not given directly, but we can find it since the kinetic energy (KE) is related to velocity (v) by the equation:

KE = 0.5 x Mass x Velocity^2

By rearranging this, we get:

Velocity = sqrt((2 x KE) / Mass)

Once we have the velocity, we can calculate the impulse and thus the force, given that we know the time is 0.3 seconds.

The correct calculation involves solving for the velocity first, and then using that to find the force using the impulse equation, with the time. None of the presented options are correct without the vehicle's initial velocity, which is required to find the answer.