You are driving your car uphill along a straight road. Suddenly, you see a car run a red light...

Friction:

The frictional force acts such that it reduces the velocity of an object.

The direction of the frictional force and the initial velocity of the object are opposite.

Given:

• The mass of the car is {eq}m = 932\ \text{kg} {/eq}.
• The inclination angle is {eq}\theta = 10^\circ {/eq}.
• The stopping distance is {eq}s = 30.5\ \text{m} {/eq}.
• The coefficient of kinetic friction between the tires and the road is {eq}\mu_k = 0.60 {/eq}.
• Let the initial speed of the car be {eq}v {/eq}.

The initial kinetic energy of the car is equal to the sum of the work done by the frictional force on the car and the final gravitational potential energy.

\begin{align} 0.5\ m\ v^2 &= \mu_k\ m\ g \ s\ \cos\theta + m\ g \ h\\ 0.5\ v^2 & = \mu_k\ g \ s\ \cos\theta + g \ h\\ 0.5\ v^2 & = \mu_k\ g \ s\ \cos\theta + g \ s\ \sin\theta\\ 0.5\ v^2 & = (0.60)\ (9.81\ \text{m/s}^2)\ (30.5\ \text{m})\cos\ 10^\circ + (9.81\ \text{m/s}^2)\ (30.5\ \text{m})\ \sin\ 10^\circ\\ 0.5\ v^2 & = 176.8\ \rm{m^2/s^2} + 51.96\ \rm {m^2/s^2}\\ \implies v &= 21.4\ \text{m/s}\\ \end{align}.

The car was speeding so it is not worth fighting the ticket in court.

Characteristics & Effects of Friction

from

Chapter 5 / Lesson 10
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Friction is the force that resists motion. An object's weight and surface material can affect the amount of friction present. Learn how to increase and decrease friction as well as the difference between static and kinetic friction.