# Did I solve this inclined plane problem correctly?

• QuarkCharmer
In summary, a block slides down an inclined plane at an initial velocity of 5 and stops after traveling a distance of 0.302 meters.
QuarkCharmer

## Homework Statement

I took a test today and I simply have to know if I got this question right! Otherwise it will haunt me for the whole weekend.

A block is at the bottom of an inclined plane with angle 30 from the horizontal. The block has an initial velocity of 5 (from pushing or something, I forget), and the kinetic friction constant is 0.4. What distance does it travel before it stops?

I have no idea why they put that height of 10m in the figure. I didn't use it at all.

## The Attempt at a Solution

I did my free-body-diagram like so:

(I forgot to add to that image, I made positive x to the right, and positive y up)

Then I went to work on Newtons second law to see what I could get.

$ƩF_{x} = ma$

$0 - mgsin(30) - f_{k} = ma$

$-mgsin(30) - \mu_{k}N = ma$

$-mgsin(30) - \mu_{k}mgcos(30) = ma$

$-mgsin(30) - (0.4)mgcos(30) = ma$

$-gsin(30) - (0.4)gcos(30) = a$ //Divided out the mass

$-(9.8)sin(30) - (0.4)(9.8)cos(30) = a$

$-8.29 = a$

Then, using kinematics:

$\upsilon_{f} = \upsilon_{i} + 2a \Delta x$

$0 = 5 + 2(-8.29) \Delta x$

$-5 = 2(-8.29) \Delta x$

$\frac{-5}{2(-8.29)} = \Delta x$

$0.302 = \Delta x$

So my solution was 0.302 meters. I may have made a mistake re-working this directly in LateX, but if that is the right idea for this problem I should have got that one on the test. Was I incorrect? I also made sure to specify that my delta x was across the hyp of the inclined plane.

Shouldn't that kinematic formula be:

$${\upsilon_{f}}^2 = {\upsilon_{i}}^2 + 2a \Delta x$$

gneill said:
Shouldn't that kinematic formula be:
Yes, it should be. I didn't check OP's working; I calculated independently.

Amazingly, I overlooked squaring the 5, in effect the same mistake, so my value is out by a factor of 5. My answer is now 1.5m up the slope.

Thanks for pointing out QuarkCharmer's mistake, it made me review my working.

Oh yeah, you are right haha. I confused it with the one that is:
v_f = V_i + at

But I am sure I used the correct one on the test (I specifically remember writing 0^2 as one line). I just did this one from what I could remember in the physicsforum.com input box.

## What is "Physics 1 Test Problem"?

"Physics 1 Test Problem" is a commonly used term for a test or exam that covers the basic principles and concepts of physics, typically at an introductory or first-year level.

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Topics commonly covered in a Physics 1 test problem include mechanics, motion, forces, energy, thermodynamics, waves, electricity, magnetism, and optics.

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To prepare for a Physics 1 test problem, it is important to review and understand the fundamental concepts and equations, practice solving problems, and familiarize yourself with the format of the test. You can also seek additional resources such as textbooks, online tutorials, and study groups.

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Some common mistakes students make on Physics 1 test problems include not fully understanding the problem, using incorrect equations or variables, making calculation errors, and not showing all steps of their work. It is important to read the problem carefully and double check your work to avoid these mistakes.

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To improve your performance on Physics 1 test problems, it is important to regularly practice solving problems and seek help when needed. You can also try to understand the underlying concepts and connections between different topics in physics, as well as identify and work on any weaknesses you may have. Additionally, make sure to manage your time effectively during the test and stay calm and focused.

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