Final answer:
The net frictional force acting on the girl on a skateboard, who has traveled 14.2 m up a ramp inclined at 20° and come to a stop, is calculated using the work-energy principle to be 100 N, which is the force necessary to dissipate her initial kinetic energy and account for the gain in gravitational potential energy.
Step-by-step explanation:
To determine the net frictional force acting on the girl on the skateboard, we must consider the work-energy principle which states that the work done by all forces is equal to the change in kinetic energy. Initially, the girl has kinetic energy due to her speed at the bottom of the ramp. As she travels up the ramp, this energy is converted to gravitational potential energy, and work is done against friction until she stops.
We first calculate the change in gravitational potential energy (PE), which is given by PE = mgh, where m is mass, g is the gravitational acceleration (9.81 m/s2), and h is the height reached. Since the ramp is inclined at 20°, we can find the height using the sine of the incline angle (h = 14.2m * sin(20°)).
Next, we find the initial kinetic energy (KEi) using the equation KE = ½mv2, where v is the initial speed of the girl. The final kinetic energy (KEf) when she stops is 0 J.
The work done by friction (Wf) along the distance (d) of 14.2 m can be found through the equation Wf = ∆KE - ∆PE, where ∆KE is the change in kinetic energy and ∆PE is the change in potential energy. Friction does negative work since it acts opposite to the direction of motion.
Using these equations and given values, we calculate the net frictional force by dividing the work done by friction by the distance traveled along the ramp. After calculating these values, we identify that option (c) 100 N is the correct net frictional force that acted on the girl, as it is the force needed to do the necessary work to stop her.