A 50 kg skier leaves the top of a 10 m high frictionless slope (point "a") from rest and reaches the bottom of the slope (point “b") with a speed v. He subsequently continues sliding on level ground to a full stop to a point “c" due to friction (i.e. µ = 0.2 on the level ground). a. Write an expression for the total mechanical energy of the skier at point “a". b. Write an expression for the total mechanical energy of the skier at point “". c. Use the Work-Energy Theorem to determine the work done from point “b" to point "c".

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A 50 kg skier leaves the top of a 10 m high frictionless slope (point "a") from rest and
reaches the bottom of the slope (point "") with a speed v,. He subsequently
continues sliding on level ground to a full stop to a point "c" due to friction (i.e.
0.2 on the level ground).
a. Write an expression for the total mechanical energy of the skier at point "a".
b. Write an expression for the total mechanical energy of the skier at point "b".
c. Use the Work-Energy Theorem to determine the work done from point “b" to
point “c".
Transcribed Image Text:A 50 kg skier leaves the top of a 10 m high frictionless slope (point "a") from rest and reaches the bottom of the slope (point "") with a speed v,. He subsequently continues sliding on level ground to a full stop to a point "c" due to friction (i.e. 0.2 on the level ground). a. Write an expression for the total mechanical energy of the skier at point "a". b. Write an expression for the total mechanical energy of the skier at point "b". c. Use the Work-Energy Theorem to determine the work done from point “b" to point “c".
Expert Solution
Step 1

Given:

The mass of the skier is 50 kg.

The height of the friction-less slope is 10 m.

The speed of skier at point 'b' is vb.

The friction coefficient of the ground is 0.2.

Calculation:

a)

When the skier is at point 'a', his initial velocity is zero and thus, the total mechanical energy of the skier is equal to the potential energy of the skier.

Write the expression for the mechanical energy at point 'a'.

Ea=mgh                                                                                                                 .....(1)

Here, Ea is the mechanical energy of skier at point 'a', m is the mass, g is the acceleration due to gravity and h is the height.

Substitute 50 kg for m, 9.8 ms2 for g, and 10 m for h in the above expression.

Ea=50 kg9.8 ms210 m=4900 J

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