What did I do wrong? (Newton's Second Law)

[glenohumeral13]

Homework Statement

(This is a problem I made up, so if the problem is with the problem, let me know.)
A 500N ball is being pushed down a carpeted decline of 24° to the horizontal. It starts from 1 m/s and ends the 20 foot (6.1 m) decline at 32 m/s. What is the coefficient and force of kinetic friction and applied force?

Homework Equations

I used:
F_g = ma_g, F = ma, a = μ_kg, and v_i = √(v_f² - (2ad)).

The Attempt at a Solution

F_g = ma_g
50N = m(9.81)
m = 5kg
v_i = √(v_f² - (2ad))
1 = √(32² - 2a(6.1))
1 = √(1024 - 12.2a)
1 = √(1011.8a)
1 = 38√(a)
1/38 = √(a)
.02² = a
a = .0004 m/s²
F = ma
F = 5*.0004
F = .002N
a = μ_kg
.0004 = μ_k(9.81)
μ_k = .000040775

 

[CWatters]

Does that value for "a" seem reasonable to you?

Spoiler

I know the equation as...

vf² = vi² + 2ad

2ad = vf² - vi²

a = (vf² - vi²)/2d

a = (1024 - 1) / (2*6.1)
= 84m/s²

 

[CWatters]

PS: It may not be your only error. I haven't checked.

 

[glenohumeral13]

Does that value for "a" seem reasonable to you?

Spoiler

I know the equation as...

vf² = vi² + 2ad

2ad = vf² - vi²

a = (vf² - vi²)/2d

a = (1024 - 1) / (2*6.1)
= 84m/s²

Thanks.

 

[HalfLostAndSearching]

It seems like you have made a few errors in your calculations. First, when calculating the mass of the ball, you used the force of gravity (Fg) instead of the weight (W = mg). This would give you a mass of 50 kg instead of 5 kg. Additionally, in your attempt at a solution, you used the wrong formula for the initial velocity (vi). Instead of using the equation for final velocity (vf), you should use the equation vi = √(vf2 - 2ad), since the ball starts from rest. This would give you a value of vi = 31.9 m/s, which is close to the given value of 32 m/s.

Next, when solving for the coefficient of kinetic friction (μk), you used the acceleration (a) instead of the coefficient of friction (μk) in your equation. The correct equation should be μk = a/g, where g is the acceleration due to gravity (9.81 m/s2). This would give you a value of μk = 0.0000408, which is close to your value of 0.000040775.

Finally, when calculating the applied force, you used the incorrect mass of 5 kg instead of the correct mass of 50 kg. Therefore, the correct value of the applied force would be F = ma = 50 * 0.0004 = 0.02 N.

In summary, it seems like you made a few mistakes in your calculations. It is important to double check your equations and make sure you are using the correct values and formulas. Keep practicing and you will improve your understanding of Newton's Second Law. Good luck!