Law of Conservation of Energy of a skier

In summary, a skier with a mass of 55.0 kg slides down a slope 11.7 m long with an initial speed of 65.7 cm/s and a final speed of 7.19 m/s. The angle theta of the slope can be determined from the law of conservation of energy, using the equation Et1 = Et2. However, the friction force of 41.5 N needs to be taken into account, which results in a different angle of 17.5 degrees. The work done by friction on the skier causes a decrease in mechanical energy (KE + PE), as work is negative if the force is opposite the displacement.
  • #1
tongtong
2
0
A skier of mass 55.0 kg slides down a slope 11.7 m long, inclined at an angle theta to the horizontal. The magnitude of the kinetic friction is 41.5 N. The skier's initial speed is 65.7 cm/s and the speed at the obttom of the slope is 7.19 m/s. Determine the angle theta from the law of conservation of energy. Air reistance is negligible.

The answer is 17.5 degrees, but the work is hard for me to start at.
From what I've learned, we use Et1 = Et2, and I can find theta from 11.7 sin theta which is delta y. I get 12.9 degrees from this. I know this is incorrect, and the friction force needs to be added in somewhere, I just don't know where.
 
Physics news on Phys.org
  • #2
Originally posted by tongtong
I know this is incorrect, and the friction force needs to be added in somewhere, I just don't know where.
If it wasn't for friction, the mechanical energy (KE + PE) would be conserved. The change in KE + PE (a decrease, of course) is equal to the work done by friction on the skier. (Don't forget that work is negative if the force is opposite the displacement.)
 
  • #3


The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one form to another. In the case of the skier sliding down the slope, the initial potential energy at the top of the slope is converted into kinetic energy as the skier accelerates down the slope. This kinetic energy is then converted back into potential energy as the skier reaches the bottom of the slope.

To determine the angle theta from the Law of Conservation of Energy, we can use the equation Et1 = Et2, where Et1 is the initial total energy (potential + kinetic) and Et2 is the final total energy (potential + kinetic). In this case, the initial energy is purely potential energy at the top of the slope, and the final energy is a combination of potential and kinetic energy at the bottom of the slope.

Et1 = mgh = (55.0 kg)(9.8 m/s^2)(11.7 m) = 6452.1 J
Et2 = (1/2)mv^2 + mgh = (1/2)(55.0 kg)(7.19 m/s)^2 + (55.0 kg)(9.8 m/s^2)(0 m) = 2285.4 J

Setting Et1 equal to Et2, we can solve for the angle theta:

Et1 = Et2
mgh = (1/2)mv^2 + mgh
mgh - mgh = (1/2)mv^2
0 = (1/2)mv^2
0 = (1/2)(55.0 kg)(7.19 m/s)^2
0 = 2285.4 J

Solving for theta, we get:

theta = sin^-1 (v^2/2gh)
theta = sin^-1 [(7.19 m/s)^2/(2)(9.8 m/s^2)(11.7 m)]
theta = 17.5 degrees

Therefore, the angle theta from the Law of Conservation of Energy is 17.5 degrees. This accounts for the effect of friction, as it is included in the initial potential energy at the top of the slope.
 

What is the Law of Conservation of Energy?

The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

How does the Law of Conservation of Energy apply to a skier?

When a skier is skiing down a slope, their potential energy (due to their position on the slope) is transformed into kinetic energy (due to their motion). As the skier moves down the slope, their kinetic energy decreases while their potential energy increases until they reach the bottom of the slope where all of their kinetic energy has been converted back into potential energy.

Does the Law of Conservation of Energy only apply to skiers going downhill?

No, the Law of Conservation of Energy applies to all forms of energy and can be observed in various aspects of a skier's movements. For example, when a skier is pushing off from the ground to gain momentum, their mechanical energy (a combination of potential and kinetic energy) is being conserved.

What factors affect the conservation of energy for a skier?

The conservation of energy for a skier is affected by several factors such as the slope of the hill, the skier's mass, the air resistance, and the friction between the skis and the snow. These factors can impact the amount of potential and kinetic energy the skier has and how it is transformed throughout their movements.

Can the Law of Conservation of Energy be violated?

No, the Law of Conservation of Energy is a fundamental law of physics and has been observed to hold true in all natural phenomena. While energy can be transformed from one form to another, the total amount of energy remains constant. Violations of this law would require energy to be created or destroyed, which has never been observed.

Similar threads

  • Introductory Physics Homework Help
2
Replies
55
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
850
  • Introductory Physics Homework Help
Replies
5
Views
971
  • Introductory Physics Homework Help
Replies
1
Views
934
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
7K
  • Introductory Physics Homework Help
Replies
3
Views
603
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top