A skier of mass 110 kg travels down a frictionless ski trial. a.) If the top of the trail is a height 200m above the bottom, what is the work done by gravity on the skier? b.) Find the velocity of the skier when he reaches the bottom of the ski trail. Assume he starts form rest.
c.) Suppose the ski trail is NOT frictionless. Find the work done by gravity on the skier in this case.
I solved part a.) as W=Force times displacement, W=(9.8)(200)=1960 Joules
Part b.) I solved as V= sqrt(2gh), so sqrt((2)(9.8)(200)),V=62.6 m/s.
I am confused as to part c, becasue I can't figure out what the difference is between work done by gravity on friction vs. nonfriction. ?
a) m g h = 110 * 9.81 * 200 Joules
(you left the mass out)
b) m g h = (1/2) m v^2
c) The work done by gravity is the same, force of gravity times distance down.
The work done by friction makes the kinetic energy (speed) less at the bottom. It does not change the change in potential from top to bottom.
Well, when it comes to the work done by gravity, the presence of friction can make a difference. In the case of a frictionless ski trail, there is no loss of energy due to friction, so all the work done by gravity goes into the skier's kinetic energy. However, if there is friction on the ski trail, some of the skier's energy will be lost to friction as heat. So, the work done by gravity in this case will be less than in the frictionless case.
To calculate the work done by gravity on the skier in the presence of friction, you'll need to know the coefficient of friction and the length of the ski trail. From there, you can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Unfortunately, you haven't provided the coefficient of friction or the length of the ski trail, so I can't give you an exact answer. But remember, when there's friction, gravity will do less work on the skier because some of the energy is lost to heat.
In part c, the difference between a frictionless ski trail and a ski trail with friction is that when there is friction, some of the energy of the skier's motion will be dissipated as heat. This means that the work done by gravity on the skier in the presence of friction will be lower than in the frictionless case.
To find the work done by gravity on the skier in the presence of friction, you need to consider the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Since the skier starts from rest, the initial kinetic energy is zero. Therefore, the work done by gravity on the skier is equal to the final kinetic energy of the skier.
To find the final kinetic energy, you can use the equation for kinetic energy: KE = (1/2)mv^2, where m is the mass of the skier and v is the velocity of the skier.
Since the skier starts from rest, the initial velocity is zero. Using the equation for velocity in terms of height and acceleration due to gravity (v = sqrt(2gh)), you can find the final velocity, which will be the velocity of the skier at the bottom of the ski trail.
Then, you can calculate the final kinetic energy using the equation for kinetic energy, and that will be equal to the work done by gravity on the skier in the presence of friction.
In part c), you are asked to find the work done by gravity on the skier when the ski trail is not frictionless. To understand the difference between the work done by gravity with and without friction, we need to consider the concept of mechanical energy.
When the ski trail is frictionless, all of the skier's initial potential energy at the top of the trail is converted into his kinetic energy when he reaches the bottom. There is no external force (like friction) acting on the skier, so the work done by gravity is equal to the change in potential energy, which we calculated as 1960 Joules in part a).
However, when there is friction on the ski trail, some of the skier's initial potential energy is dissipated as thermal energy due to the work done by the frictional force. As a result, the work done by gravity will be less than the change in potential energy. This means that not all of the potential energy is converted into kinetic energy.
To determine the work done by gravity in the presence of friction, you need additional information about the nature and magnitude of the frictional force. This could include factors such as the coefficient of friction, the length of the ski trail, and the speed of the skier. With this information, you can calculate the work done by the frictional force and subtract it from the change in potential energy to find the net work done by gravity on the skier.
Without this additional information, it is not possible to calculate the exact work done by gravity when there is friction on the ski trail.