Finding initial velocity given angle, friction, and distance

In summary: Yes, thank you again and I will be on here probably a lot. (Mechanical Engineering major, just starting my physics sequence.)
  • #1
jhawks8
9
0

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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  • #2
Can you find the acceleration of Johnny down the slope?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.

[tex]\sum[/tex]Fx=mgsin20-Fk

[tex]\sum[/tex]Fy=n-mgcos20=0
 
  • #8
jhawks8 said:
[tex]\sum[/tex]Fx=mgsin20-Fk

[tex]\sum[/tex]Fy=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?
 
  • #9
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.)
 

1. What is the formula for finding initial velocity given angle, friction, and distance?

The formula for finding initial velocity is:
v0 = √(d / sin2θ - 2μcosθ sinθ)
Where v0 is the initial velocity, d is the distance, θ is the angle, and μ is the coefficient of friction.

2. How do I determine the angle and coefficient of friction for this calculation?

The angle can be determined by using a protractor or by measuring the angle from a diagram. The coefficient of friction can be found in reference tables or by conducting experiments.

3. Can this formula be used for any type of motion or only for objects moving horizontally?

This formula can only be used for objects moving horizontally. For objects moving at an angle, the formula would need to be modified to take into account the vertical and horizontal components of the initial velocity.

4. Is this formula affected by air resistance?

Yes, this formula does not account for air resistance. If air resistance is present, the initial velocity calculated using this formula will be slightly higher than the actual initial velocity.

5. Can I use this formula to find the initial velocity of a moving object if I know the final velocity?

No, this formula can only be used to find the initial velocity given the angle, friction, and distance. If the final velocity is known, other formulas such as the equations of motion or the law of conservation of energy can be used to find the initial velocity.

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