4.40 An advertisement claims that a particular automobile can stop on a dime. Wh

Question

4.40
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 970kg traveling initially at a speed of 41.0km/h in a distance equal to the diameter of a dime, which is 1.8cm 4.40
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 970kg traveling initially at a speed of 41.0km/h in a distance equal to the diameter of a dime, which is 1.8cm

Explanation / Answer

Use the work energy theorem, and assume that the stopping force is constant.

Initially, the kinetic energy is
KEi = 1/2*m*vi^2

Finally, the kinetic energy = 0, because it is at rest
KEf = 0

The change in kinetic energy, ?KE = KEf - KEi

Thus:
?KE = -1/2*m*vi^2

As per work energy theorem, equate ?KE to the work done on the car by the stopping force:
W = ?KE

Work done by an assumed constant stopping force:
W = Fnet*d

Substitute:
Fnet*d = -1/2*m*vi^2

Solve for Fnet:
Fnet = -1/2*m*vi^2/d

Data:
d:=0.018 m; m:=880 kg (that is lightweight for a car); vi:=41*10/36 meters/second (10/36 is the conversion factor from kmph to meters/second);

Result:
Fnet = -3.171 MegaNewtons

The negative implies that the force is opposite the distance traveled, well that's obvious.

Most likely, this car cannot literally stop on dime...unless it is in a fatal accident. People in the car are subject to accelerations 3603 times the strength of Earth's gravity during this stopping, thus the seat belts will cut their chests and waists, having them smash through the windshield.

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