What Is the Correct Formula for Normal Force on a Sloped Surface?

In summary, when a skier of mass 51.4 kg is skiing down a slope of constant angle 26◦ with the horizontal, the normal force exerted by the skis (neglecting friction) can be calculated using the equation F=m*g*cos26, where g is the acceleration of gravity (9.8 m/s^2). This is because the normal force is always perpendicular to the surface the object is on, and in this case, the slope is at a 26 degree angle with the horizontal. It is important to consider the components of the force, as in this case, the normal force is not equal to either m*g*cos0 or m*g*sin0.
  • #1
Robertoalva
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1. A skier of mass 51.4 kg comes down a slope of constant angle 26◦ with the horizontal. What force normal to the slope is exerted by the skis (neglect friction)? The acceleration of gravity is 9.8 m/s^2.



Homework Equations



F=ma

The Attempt at a Solution



my intuitions tell me to do this:

F=m*g*cos26

am i wrong?
 
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  • #2
i already did this!
 
  • #3
Robertoalva said:
1. A skier of mass 51.4 kg comes down a slope of constant angle 26◦ with the horizontal. What force normal to the slope is exerted by the skis (neglect friction)? The acceleration of gravity is 9.8 m/s^2.



Homework Equations



F=ma

The Attempt at a Solution



my intuitions tell me to do this:

F=m*g*cos26

am i wrong?

A hint on how to think:

The answer is either m*g*cos26 or m*g*sin26

Suppose the slope was ≈ 0 degrees; one of m*g*cos0 or m*g*sin0 is zero.

If the slope was ≈ 0 degrees, would the normal force be ≈ 0 ?

That shows which one is NOT the answer.
 

1. What is the force that allows a skier to move down a slope?

The force that allows a skier to move down a slope is gravity. As the skier travels downhill, the force of gravity pulls them towards the Earth, causing them to accelerate and gain speed.

2. How does the weight of a skier affect their movement down a slope?

The weight of a skier plays a significant role in their movement down a slope. A heavier skier will have a greater force of gravity pulling them down the slope, causing them to travel faster. On the other hand, a lighter skier will have a weaker force of gravity and may move down the slope at a slower pace.

3. What other forces act on a skier as they move down a slope?

In addition to gravity, there are two other forces that act on a skier as they move down a slope: friction and air resistance. Friction is the force between the skier and the snow, which helps to slow down their movement. Air resistance, also known as drag, is the force of air pushing against the skier as they move downhill.

4. How does the angle of the slope affect a skier's speed?

The angle of the slope has a significant impact on a skier's speed. A steeper slope will result in a greater force of gravity, causing the skier to accelerate and move faster. Conversely, a flatter slope will have a weaker force of gravity and will result in a slower speed for the skier.

5. How does a skier use their body to control their movement down a slope?

A skier can use their body to control their movement down a slope in several ways. They can shift their weight to one side or the other to turn, use their poles to push off and gain speed, and adjust their body position to increase or decrease air resistance. Additionally, they can use their muscles to absorb shocks and maintain balance while navigating down the slope.

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