Physics q- friction in BR passage

[Ari1584]

In section 2 of berkeley review, passage 7, the passage describes a skiier being pulled up a mountain by a tow rope. There are a couple of questions where we have to write out the forces acting on the skiier. What i dont get is that i thought friction opposed the motion of the skiier.

-For #43 it asks to write out the equation for the minimum tension the tow rope must provide to keep the skier moving up the hill. The skiier is on a picture of an inclined plane with the tow rope attached, pulling him up. The forces acting are the Tension in the rope up the hill, friction down the hill, normal force perpendicular and gravitational force straight down. I get all that.
But THEN, for #44, it says "a skier has to side step up a hill and turns her skis perpendicularl to the hill and makes a series of small steps up the hill. The max steepness of a hill that a skier can side step is determined by?

In the answer diagram, they drew the forces and they have the friction force going IN the direction of motion. I thought its supposed to be the other way?

-Also for #46 it says a skier skies down a curved hill. As the skier skis down the hill, which of the following concering his acc and speed is true?

a. the speed decreases and acc increases
b. speed increases and acc decreases
c. both speed and acc increase
d. both the speed and acc decrease

I thought that since the skiier is going down, the angle of inclination is getting smaller so the acceleration is decreasing, which means speed decreases. The answer is that the angle is getting BIGGER. How is that possible?? Isn't going from the top of something to the bottom of an inclined plane means that the angle is getting smaller? what am i missing here...its prob really simple and i just dont understand it!

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[BerkReviewTeach]

-For #43 it asks to write out the equation for the minimum tension the tow rope must provide to keep the skier moving up the hill. The skiier is on a picture of an inclined plane with the tow rope attached, pulling him up. The forces acting are the Tension in the rope up the hill, friction down the hill, normal force perpendicular and gravitational force straight down. I get all that.
But THEN, for #44, it says "a skier has to side step up a hill and turns her skis perpendicularl to the hill and makes a series of small steps up the hill. The max steepness of a hill that a skier can side step is determined by?

In the answer diagram, they drew the forces and they have the friction force going IN the direction of motion. I thought its supposed to be the other way?

Good observation!

The difference netween the questions is that in question #43, the skier is sliding up the mountain, so there is a kinetic frictional force that opposes the direction of the skier's motion. Because the skier is being towed up the hill at an angle equal to the incline, there a friction force down the montain at the angle of the incline. It seems like that part sits fine with you

In question #44, the difference is that the skier is not sliding, but is stepping. In order to push off, there has to be a static friction pushing back against the foot of the skier. It's always a weird concept at first glance that a static frictional force can accelerate you from rest, but if you think about what happens when you walk, it has to be static friction. You start from rest and begin to move, so there must be a force accelerating you forward from rest. That force is static friction. As long as your feet don't slip (in which case the friction becomes kinetic rather than static), then it's a static friction counter force that opposes your push off and is responsible for accelerating you. That is why its so hard to start running on ice or a waxed floor wearing socks. But I digress. The frictional force felt by the skier that is walking sideways up the hill is a static friction, because there is no sliding.

I hope that explains the difference.

 

[BerkReviewTeach]

Also for #46 it says a skier skies down a curved hill. As the skier skis down the hill, which of the following concerning his acc and speed is true?

a. the speed decreases and acc increases
b. speed increases and acc decreases
c. both speed and acc increase
d. both the speed and acc decrease

I thought that since the skiier is going down, the angle of inclination is getting smaller so the acceleration is decreasing, which means speed decreases. The answer is that the angle is getting BIGGER. How is that possible?? Isn't going from the top of something to the bottom of an inclined plane means that the angle is getting smaller? what am i missing here...its prob really simple and i just dont understand it!

If you look at the curvature of the slope in the picture, you'll see that it's flat at the top and gradually gets steeper and steeper as you go down. If you think of the scream one would make as they went over the edge of such a cliff, you would have to agree that at first it's no big deal, but very quickly they pick up a bunch of speed and are flying straight down hill.

The F = mg sin(theta), so a = g sin(theta). The angle gets steeper and steeper as you descend, so the value of g sin(theta) increases as you go down the hill, meaning that a is increasing. This matches our conceptual perspective.

Regardless of what acceleration does, no matter what the skier is pointing downhill the entire time, so they are being accelerated continually, meaning they will always be speeding up (assuming friction doesn't catch up to them).