Question

For part 3 of 3, just enter magnitude (positve number)

A 1933 kg car has a speed of 14 m/s when it hits a tree. The tree doesn’t move and the car comes to rest.

Find the change in kinetic energy of the car. Answer in units of J.
Find the amount of work done by the car as its front is pushed in.
Answer in units of J.

Find the magnitude of the force that pushed the front of the car in by 38 cm.
Answer in units of N.

Answer 1

The change in kinetic energy of the car is -189434 joules.

The work done by the car is 189434 joules.

The magnitude of the force that pushed the front of the car is 498510.526 newtons.

Step-by-step explanation:

Given that the car is moving on a horizontal ground, by the Principle of Energy Conservation and the Work-Energy Theorem we get the following identity:

`\Delta K+\Delta W = 0` (1)

Where:

`\Delta K` - Change in the translational kinetic energy of the car, measured in joules.

`\Delta W` - Work done by the car, measured in joules.

By applying the defintions of translational kinetic energy and work, we expand and simplify the resulting equation:

`(1)/(2)\cdot m \cdot (v_(f)^(2)-v_(o)^(2))+F\cdot \Delta s = 0` (2)

Where:

`m` - Mass, measured in kilograms.

`v_(o)`,
`v_(f)` - Initial and final speeds of the car, measured in meters per second.

`F` - Force exerted by the car, measured in newtons.

`\Delta s` - Travelled distance of the front of the car, measured in meters.

The change in the kinetic energy of the car and the work done by the car are, respectively:
`(v_(o) = 14\,(m)/(s), v_(f)= 0\,(m)/(s), m = 1933\,kg, \Delta s = 0.38\,m)`

Translational kinetic energy

`\Delta K = (1)/(2)\cdot m\cdot (v_(f)^(2)-v_(o)^(2))`

`\Delta K = (1)/(2)\cdot (1933\,kg)\cdot \left[\left(0\,(m)/(s) \right)^(2)-\left(14\,(m)/(s) \right)^(2)\right]`

`\Delta K = -189434\,J`

Work done by the car

`\Delta W = -\Delta K`

`\Delta W = 189434\,J`

Magnitude of the force

`F = (\Delta W)/(\Delta s)`

`F = (189434\,J)/(0.38\,m)`

`F = 498510.526\,N`

The change in kinetic energy of the car is -189434 joules.

The work done by the car is 189434 joules.

The magnitude of the force that pushed the front of the car is 498510.526 newtons.