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 850Kg traveling initially at a speed of 43.0 km/h in a distance equal to the diameter of a dime, which is 1.8cm ?
The "work against friction", F * X, would have to equal the initial kinetic evergy, (1/2) M V^2.
F = M V^2/(2 X)
Convert 43.0 km/h to ____m/s, X to 0.018 m, and solve for F in Newtons.
(1 Newton = 0.2248 pounds of force)
3493065
281916.7N
To find the net force required to stop the automobile, we can use the concept of kinetic energy and work done. Here's how to calculate it step by step:
1. Convert the given speed from km/h to m/s: Since 1 km/h is equal to 0.2778 m/s, the speed of the automobile is 43.0 km/h * 0.2778 m/s = 11.9444 m/s.
2. Convert the given distance from centimeters to meters: The diameter of a dime is 1.8 cm, which is equal to 0.018 meters.
3. Calculate the initial kinetic energy (KE) of the automobile: The formula for kinetic energy is KE = (1/2) * mass * velocity^2. Plugging in the values, we have KE = (1/2) * 850 kg * (11.9444 m/s)^2.
4. Calculate the work done (W) to stop the automobile: The formula for work done is W = KE_final - KE_initial, where KE_final = 0 since the automobile needs to stop. Therefore, W = 0 - KE_initial.
5. Determine the net force (F) required using the work-energy theorem: The work done is equal to the net force multiplied by the distance. Therefore, W = F * distance. Rearranging the equation, we can solve for the net force F = W / distance.
Now let's calculate the values:
- Initial kinetic energy (KE_initial):
KE_initial = (1/2) * 850 kg * (11.9444 m/s)^2 = 57,512.3256 J
- Work done (W):
W = 0 - KE_initial = -57,512.3256 J
- Net force (F):
F = W / distance = (-57,512.3256 J) / 0.018 m = -3,195,129.2 N
Note that the negative sign indicates that the direction of the force needed would be opposite to the direction of motion of the automobile.
Therefore, to stop the automobile and meet the claim of "stopping on a dime," a net force of approximately 3,195,129.2 Newtons is required.