Question

A skier glides down an incline plane of length L starting from rest. The ski slope makes an angle ? with the horizontal. What is the speed (v) of the skier at the bottom of the plane? Choose your coordinate system so that it is level with the ground as shown. Calculate the total mechanical energy of the skier at the top of the slope using the following: E_{T,M} = U_G + K. Keep in mind that skier starts from rest and while you don't know the actual y value for calculating the potential energy, you can write the potential energy in terms of L, the length of the hill and the angle ?. E_{T,M, initial} = ________________________________ Calculate the total mechanical energy at the bottom of the hill using the following: E_{T,M} = U_G + K. E_{T,M, final} = ________________________________ Using what you saw in the video, specifically that when only conservative forces are acting, the total mechanical energy, E_{T,M} is constant, find the skier's velocity at the bottom of the hill v_{final} = ________________________________ Now place your coordinate system at the skier's starting position as shown, and repeat your calculations. (Hint: it is perfectly fine to have a negative value for your potential energy as we saw in the video when we placed the coordinate system at the maximum height that the ball attained). If you are unsure of this, go back to the video on Potential Energy. E_{T,M, initial} = ________________________________ E_{T,M, final} = ________________________________ v_f = ________________________________

          A skier glides down an incline plane of length L starting from rest. The ski slope makes an angle ? with the horizontal. What is the speed (v) of the skier at the bottom of the plane? Choose your coordinate system so that it is level with the ground as shown.

Calculate the total mechanical energy of the skier at the top of the slope using the following: E_{T,M} = U_G + K. Keep in mind that skier starts from rest and while you don't know the actual y value for calculating the potential energy, you can write the potential energy in terms of L, the length of the hill and the angle ?.

E_{T,M, initial} = ________________________________

Calculate the total mechanical energy at the bottom of the hill using the following: E_{T,M} = U_G + K.

E_{T,M, final} = ________________________________

Using what you saw in the video, specifically that when only conservative forces are acting, the total mechanical energy, E_{T,M} is constant, find the skier's velocity at the bottom of the hill

v_{final} = ________________________________

Now place your coordinate system at the skier's starting position as shown, and repeat your calculations. (Hint: it is perfectly fine to have a negative value for your potential energy as we saw in the video when we placed the coordinate system at the maximum height that the ball attained). If you are unsure of this, go back to the video on Potential Energy.

E_{T,M, initial} = ________________________________

E_{T,M, final} = ________________________________

v_f = ________________________________

A skier glides down an incline plane of length L starting from rest. The ski slope makes an angle ? with the horizontal. What is the speed (v) of the skier at the bottom of the plane? Choose your coordinate system so that it is level with the ground as shown.

Calculate the total mechanical energy of the skier at the top of the slope using the following: ET,M = UG + K. Keep in mind that skier starts from rest and while you don't know the actual y value for calculating the potential energy, you can write the potential energy in terms of L, the length of the hill and the angle ?.

ET,M, initial =

Calculate the total mechanical energy at the bottom of the hill using the following: ET,M = UG + K.

ET,M, final =

Using what you saw in the video, specifically that when only conservative forces are acting, the total mechanical energy, ET,M is constant, find the skier's velocity at the bottom of the hill

vfinal =

Now place your coordinate system at the skier's starting position as shown, and repeat your calculations. (Hint: it is perfectly fine to have a negative value for your potential energy as we saw in the video when we placed the coordinate system at the maximum height that the ball attained). If you are unsure of this, go back to the video on Potential Energy.

ET,M, initial =

ET,M, final =

vf =

Added by David G.

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