A car is moving at a relatively slow speed, let\'s say a good running speed for

Question

A car is moving at a relatively slow speed, let's say a good running speed for a short distance sprint, when it hits a solid wall (top figure).

The car comes to a complete stop, with a somewhat shorter front section now. The driver, who was not wearing a seat belt, tries to hold himself off the steering wheel.

Let us find the necessary average force acting on the 82-kg driver that is necessary to bring him to a complete stop before hitting the steering wheel or windshield. This is also the force the driver needs to exert on the steering wheel (Newton's 3rd Law).

The distance that is available to achieve this, as we will see impossible feat, is the original distance to the steering wheel plus the amount by which the front section shortens. For now, let's assume a probably too generous distance of 1 m.

I want you to work this out two different ways:

Use your knowledge about motion at constant acceleration to find the acceleration, and then use Newton's 2nd Law to find the magnitude of the force.

Use the Work-Kinetic Energy Theorem to find the magnitude of the force.

Of course, you should expect to get the same answer with both methods. Below answer with the force in pounds (lbs).

Explanation / Answer

Here,

mass , m= 82 Kg

distance ,d = 1 m

let the constant acceleration is a

Using third equation of motion

v^2 - u^2 = 2 *a * d

let the initial velocity = 60 kmh = 16.7 m/s

16.7^2 - 0^2 = 2 * a * 1

a = 138.9 m/s^2

the acceleration is 138.9 m/s^2

magnitude of force = m * a

magnitude of force = 82 * 138.9 N

magnitude of force = 11388 N

-------------------------------

let the force is F

Using work energy theorum

F * 1 = 0.5 * 82 * 16.7^2

solving for F

F = 11388 N

the magnitude of force is 11388 N

foirce in pounds = 2560.1243 lbs

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.