Finding initial velocity given angle, friction, and distance

[jhawks8]

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?

 

[thrill3rnit3]

Can you find the acceleration of Johnny down the slope?

 

[jhawks8]

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.

 

[thrill3rnit3]

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.

 

[jhawks8]

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?

 

[thrill3rnit3]

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.

 

[jhawks8]

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.

$$\sum$$F_x=mgsin20-F_k

$$\sum$$F_y=n-mgcos20=0

 

[thrill3rnit3]

$$\sum$$F_x=mgsin20-F_k

$$\sum$$F_y=n-mgcos20=0

OK. Now F_k = μ_kN

N = mgcos20^o

F_k = μ_kmgcos20^o

substitute that to your ΣF_x equation and solve for a_x:

ΣF_x = ma_x = mgsin20^o - μ_kmgcos20^o

You see how the mass cancels out?

 

[jhawks8]

OK. Now F_k = μ_kN

N = mgcos20^o

F_k = μ_kmgcos20^o

substitute that to your ΣF_x equation and solve for a_x:

ΣF_x = ma_x = mgsin20^o - μ_kmgcos20^o

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.

 

[thrill3rnit3]

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?

 

[jhawks8]

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.

 

[thrill3rnit3]

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

 

[jhawks8]

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

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