Finding initial velocity given angle, friction, and distance

AI Thread Summary
Johnny slides down a 20-degree slope after jumping off a swing, and the problem involves calculating his initial speed and acceleration while considering friction. The coefficient of kinetic friction is 0.5, and the mass is not needed for calculations since it cancels out. The forces acting on Johnny are resolved into components along the slope and perpendicular to it, leading to equations for acceleration. The final calculations yield an acceleration of -1.25 m/s² and an initial speed of 2.96 m/s. The discussion emphasizes the importance of understanding force components and the cancellation of mass in physics problems.
jhawks8
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Homework Statement



Johnny jumps off a swing, lands sitting down on a grassy 20 degree slope, and slides 3.5m down the slope before stopping. The coefficient of kinetic friction between grass and the seat of Johnny's pants is 0.5

What was his initial speed on the grass?
 
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Can you find the acceleration of Johnny down the slope?
 
thrill3rnit3 said:
Can you find the acceleration of Johnny down the slope?

That is the part I need help with because after that I believe it is just kinematics.

I know that because it is on a slope, n should equal mgcos20, but I am very confused because I don't know what the mass of Johnny is.
 
jhawks8 said:
That is the part I need help with because after that I believe it is just kinematics.

I know that because it is on a slope, n should equal mgcos20, but I am very confused because I don't know what the mass of Johnny is.

Just work out the algebra, mass eventually cancels out.
 
thrill3rnit3 said:
Just work out the algebra, mass eventually cancels out.
I have tried doing that, but I'm just stuck there. The only way I can figure out how to get an acceleration is if n=mg but in this case it does not. Do you care to explain it to me?
 
jhawks8 said:
I have tried doing that, but I'm just stuck there. The only way I can figure out how to get an acceleration is if n=mg but in this case it does not. Do you care to explain it to me?

Make the slope your x-axis, and make the axis perpendicular to that your y-axis. That should make life easier for you. Then resolve each force into its x and y components, and do your sum of forces for each. Try that first and post what you get.
 
thrill3rnit3 said:
Make the slope your x-axis, and make the axis perpendicular to that your y-axis. That should make life easier for you. Then resolve each force into its x and y components, and do your sum of forces for each. Try that first and post what you get.

\sumFx=mgsin20-Fk

\sumFy=n-mgcos20=0
 
jhawks8 said:
\sumFx=mgsin20-Fk

\sumFy=n-mgcos20=0

OK. Now Fk = μkN

N = mgcos20o

Fk = μkmgcos20o

substitute that to your ΣFx equation and solve for ax:

ΣFx = max = mgsin20o - μkmgcos20o

You see how the mass cancels out?
 
thrill3rnit3 said:
OK. Now Fk = μkN

N = mgcos20o

Fk = μkmgcos20o

substitute that to your ΣFx equation and solve for ax:

ΣFx = max = mgsin20o - μkmgcos20o

You see how the mass cancels out?

Thank you very much, that is the help I was looking for. I was able to get an acceleration of -1.25m/s2 and the answer to the question was 2.96m/s.
 
  • #10
jhawks8 said:
Thank you very much, that is the help I was looking for. I was able to get an acceleration of -1.25m/s2 and the answer to the question was 2.96m/s.

No problem! I'm going to assume that you did the rest of the calculations correctly.

Just wondering, which part exactly were you stumped with?
 
  • #11
thrill3rnit3 said:
No problem! I'm going to assume that you did the rest of the calculations correctly.

Just wondering, which part exactly were you stumped with?

I was stumped with finding the acceleration, basically getting m to cancel out. And yes, those are correct calculations because my homework is on an online program that automatically grades you.
 
  • #12
jhawks8 said:
I was stumped with finding the acceleration, basically getting m to cancel out. And yes, those are correct calculations because my homework is on an online program that automatically grades you.

Mass usually cancels out in these types of problems, especially when it's not given to you.

Anyways I'm glad everything worked out well for you :approve:
 
  • #13
thrill3rnit3 said:
Mass usually cancels out in these types of problems, especially when it's not given to you.

Anyways I'm glad everything worked out well for you :approve:

Yes, thank you again and I will be on here probably a lot. (Mechanical Engineering major, just starting my physics sequence.)
 
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