While on a trail, a mountain biker encounters a sandy patch that is 7.1 m long. The speed of the bike entering the patch is 10.1 m/s. If the force exerted by the sand on the bike/biker system (103.8 kg) is 514 N, determine the speed of the biker when exiting the sandy patch.
Subtract the work done moving through sand (force x distance) from the initial kinetic energy. That will be the final kinetic energy,
(1/2)M Vfinal^2
Then solve for Vfinal.
To determine the speed of the biker when exiting the sandy patch, we can use the concept of conservation of energy. Here's how to get the answer:
1. First, let's consider the initial kinetic energy (KE1) of the bike/biker system when entering the sandy patch. The formula for kinetic energy is KE = 0.5 * mass * velocity^2.
KE1 = 0.5 * 103.8 kg * (10.1 m/s)^2
2. Next, let's consider the work done by the force of sand (W) on the bike/biker system. The formula for work is W = Force * distance. In this case, the force exerted by the sand on the system is 514 N, and the distance traveled through the sandy patch is 7.1 m.
W = 514 N * 7.1 m
3. Now, let's consider the final kinetic energy (KE2) of the bike/biker system when exiting the sandy patch. Since the sandy patch is a non-conservative force, some of the initial kinetic energy will be converted into work done against the force of sand. Therefore, the final kinetic energy will be less than the initial kinetic energy.
KE2 = KE1 - W
4. Finally, we can determine the speed of the biker when exiting the sandy patch using the final kinetic energy (KE2). Rearranging the formula for kinetic energy, we can solve for velocity:
KE2 = 0.5 * 103.8 kg * velocity^2
Solve for velocity:
velocity = sqrt(2 * KE2 / (103.8 kg))
By plugging in the values of KE2 and solving for velocity, we can determine the speed of the biker when exiting the sandy patch.