kinetics question (physics) please help :)

Question

Neville Longbottom was dared by his friends to go down Suicide Hill, but at point P he gets a little nervous. From point P to Q he drags a foot and creates some friction, so μk=0.13. Suppose the distance from P to Q is a horizontal 11.4 meters, Neville's mass is 40.4 kg and he has KEP=2801 Joules of kinetic energy at point P. Find his kinetic energy at point Q (KEQ).

In your answer:
give precision to 1 (no decimal needed).

Answer 1

Hi Lauren:

 

The work-(kinetic energy theorem can also be used here.  See your previous post for my description of the theorem.

 

Making the same assumption Frank mentioned, that only friction is acting along the line of displacement, the work-(kinetic) energy theorem gives:

 

W_net = W_f = KE_f - KE_i

 

W_f = F_fdcosα

 

Since friction always opposes any motion that is happening, it always points directly opposite displacement, and therefore, the angle between force and displacement is always 180^o.  So friction ALWAYS does negative work (cos(180^o) = -1).

 

W_f = -F_fd

 

F_f = μ_kN

 

where N = normal force.  On a horizontal surface, as described, where only the normal force and gravity act vertically, they must equal each other (since the net vertical acceleration is 0).  So, N = mg, and

 

F_f = μ_kmg = (0.13)(40 kg)(9.8 m/s²) = 51 N

 

Then:

 

W_f = -F_fd = -(51 N)(11.4 m) = -581 J = KE_f - KE_i

 

We are told KE_i = 2801 J.  So we have:

 

-581 J = KE_f - 2801 J

 

KE_f = -581 + 2801 = 2220 J

 

I hope this helps!  Just let me know if you have any questions about this.

 

 

Answer 2

Assuming that it's a flat surface and the only force acting on Neville is friction:

 

Friction = 40.4 * 9.8 * 0.13 = 51.4696 in the direction opposite to his movement

 

Acceleration = Friction / mass = 51.4696 / 40.4 = 1.274 m / second / second

 

KEP = 1/2 * m * v²

2801 = 1/2 * 40.4 * v²

VI² = Initial velocity squared = 5602 / 40.4 = 138.6634

 

 

Final Velocity - VF² = VI² - 2as

VF² = VI² - 2 * 1.274 * 11.4

      =  138.6634 - 22.4 * 1.274 = 138.6634 - 29.0472

      =  109.6162

 

KEQ = 1/2 * m * VF²

       = 0.5 * 40.4 * 109.6162 = 2214.247 joules