Question

A car of mass 1200 kg is traveling at 2 m/s. Then it collides with a heavy boulder in the road. During the collision, the car moves forward only 15 cm before stopping. What is the average force exerted by the boulder on the car?
1.6 x 104 N
3.2 x 104 N
5.4 x 104 N
6.5 x 105 N
1.8 x 104 N

Answer 1

Answer:

F = 1.6*10⁴ N

Explanation:

Given distance x = 0.15m, mass m = 1200kg, velocity v = 2m/s.

Unknown: force F

Force is given by Newton's law:

(1) $F = ma$

The average force to stop an object from a velocity will be the same force necessary to accelerate an object from rest to the same velocity.

The distance for an object starting from rest for a constant acceleration is given by:

(2) $x=\frac{1}{2}at^2$

The velocity for an object starting from rest for a constant acceleration:

(3) $v=at$

Using equation 2 and 3 to eliminate time t:

(4) $x=\frac{1}{2}a\frac{v^2}{a^2}=\frac{v^2}{2a}$

Solving equation 4 for the acceleration a:

(5) $a=\frac{v^2}{2x}$

Using equation1 to solve for the force F:

(6) $F=ma=\frac{mv^2}{2x}$