# F=maF=(59)(V-0)/3Solving Ski Slope Physics Problems

• kdizzle711
In summary, the skier of mass 59.0kg starts from rest at the top of a ski slope of height 70.0m. If frictional forces do −1.08×10^4J of work on her as she descends, she will be going at a velocity of 31.4 m/s at the bottom of the slope. After crossing a patch of soft snow, where the coefficient of friction is 0.180, and encountering an average force of air resistance of 170N, the skier will have a velocity of 29.5 m/s. Finally, after hitting a snowdrift and penetrating a distance of 3.00m, the average
kdizzle711

## Homework Statement

A skier of mass 59.0kg starts from rest at the top of a ski slope of height 70.0m .

## The Attempt at a Solution

If frictional forces do −1.08×10^4J of work on her as she descends, how fast is she going at the bottom of the slope?

(1/2)mV^2=mgh + (1/2)mV^2 + -1.08 x10^4
0=59*9.8*70+(1/2)(59)(v^2)+-1.08x10^4
v=31.4

Now moving horizontally, the skier crosses a patch of soft snow, where the coefficient of friction is = 0.180. If the patch is of width 65.0m and the average force of air resistance on the skier is 170N , how fast is she going after crossing the patch?

(1/2)*59*31.7=59*9.8*70+(1/2)(59)(v^2)+11.7+170
935-11.7-170=40,474+29.5v^2
V^2=
v=

Where an I going wrong with this?

C. After crossing the patch of soft snow, the skier hits a snowdrift and penetrates a distance 3.00m into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

first of all, please don't put in numbers. Use variables. The number one source of error is using numbers before having derived.

So in your first part, you have 1/2mvi^2 = 1/2mvf^2 + mgh - Et (friction). There is a flaw in your equation there. The skier didn't gain potential energy coming down the hill, and the thermal heat wasn't gained, it was lost.

Try to fix that.

Then in your second part, try doing an energy balance equation again. Try to do the first part first.

Well first off, I notice that you used the correct value of 31.7 m/s in the second part of the question, but for the first part you wrote it as 31.4 m/s. It might be a typo, but if not it'll need correcting.

For the second part of the question, start by calculating the frictional force acting on the skier using the formula:
$$F = \mu R$$

Once you have that force, you can add it to the force due to air resistance, then you can calculate the work done on the skier with:
$$W = Fd$$

Then you can subtract that from the skiers initial kinetic energy, to find the KE after the patch of soft snow and therefore also their velocity.

For the final part of the question, you know their initial velocity (the answer from part b), their final velocity (0) and the distance it takes to stop. So you'd need to calculate their deceleration with:
$$v^{2} = u^{2} + 2as$$

And then plug that into:
$$F = ma$$

yea, but lavalamp. he did the first part wrong.

While I admit that the working out could be ... improved upon. The poster did get the correct answer.

It is possible that for the work that will be handed in it was laid out correctly, since I find that when typing lots of people tend to get lazy and write things that are incorrect but where the meaning is (usually) clear.

What does U^2 and R stand for in those equations

u is initial velocity, and R is the normal force.

Thanks for all the help, I figured it out

## 1. What does the equation F=ma mean?

The equation F=ma represents Newton's Second Law of Motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). This equation is used to calculate the force necessary to move an object with a certain mass at a given acceleration.

## 2. How do I use the equation F=ma to solve ski slope physics problems?

To solve ski slope physics problems, you will need to plug in the values for mass (m) and acceleration (a) into the equation F=ma. In this specific equation for solving ski slope problems, the value for force (F) is already given as (59)(V-0)/3. By rearranging the equation to solve for V, you can find the velocity of the object on the ski slope.

## 3. What is the unit of measurement for the variables in the equation F=ma?

The unit of measurement for mass (m) is typically in kilograms (kg), while the unit for acceleration (a) is usually in meters per second squared (m/s²). This means that the unit for force (F) would be in Newtons (N).

## 4. Can the equation F=ma be applied to any object in motion?

Yes, the equation F=ma can be applied to any object in motion, as long as it is experiencing a constant acceleration. This includes objects moving on a ski slope, objects falling due to gravity, and even objects being pushed or pulled by a force.

## 5. What other factors may affect the accuracy of using the equation F=ma to solve ski slope physics problems?

Other factors that may affect the accuracy of using the equation F=ma to solve ski slope physics problems include air resistance, friction, and the shape or design of the object being used. These factors can introduce additional forces that may affect the acceleration and ultimately the calculated force needed to move the object on the ski slope.

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