Physics help i can't seem to get?

Question

An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop an automobile of mass 860 kg traveling initially at a speed of 58.0 km/h in a distance equal to the diameter of a dime, which is 1.80 cm?

so i used the formula sum of F= (m(vf^2-vi^2))/2x.

is this wrong because i keep on getting the wrong answer. please help.

Answer 1

Your formula is correct. It comes from equating the change in kinetic energy of the car with the work done in bringing the car to a stop.

The change in kinetic energy is (vf^2 - vi^2)*m/2

For a constant force, the work done is F*x (where F is the component of force parallel to the direction of motion of the car).

Equating these gives:

F*x = (vf^2 - vi^2)*m/2
F = (vf^2 - vi^2)*m/(2*x)

Plugging in the values given in the problem yields:

F = 6.201 * 10^6 N

What answer did you get?

Answer 2

The formula you are using is correct, just make sure your units are all in order.
The initial speed of the car is given in km/h, but you want it in m/s.
The diameter of the dime is given in cm, you need it in meters.


1 km = 1000 m
1 hour = 60 minutes
1 minute = 60 seconds
1 m = 100 cm

Answer 3

Looks like you have the right idea, just make sure you convert everything to meters and seconds. Here's how I would do it:

F = m [(vf^2-vi^2)/(2x)] = 860 * [(0 - 259.21)/(2 * .018) = ~ 6,200,000 N

Make sure to keep your parentheses when you punch it in your calculator, otherwise it thinks you want to multiply everything by .018 instead of divide it.

Hope this helps :)