Therefore, the coefficient of friction between the ball and the green is 1.54.

[FahimP]

Homework Statement

The greenskeepers of golf courses use a stimpmeter to determine how "fast" their greens are. A stimpmeter is a straight aluminum bar with a V-shaped groove on which a golf ball can roll. It is designed to release the golf ball once the angle of the bar with the ground reaches a value of θ = 20.0°. The golf ball (mass = 1.62 oz = 0.0459 kg) rolls 29.3 in down the bar and then continues to roll along the green for several feet. This distance is called the "reading." The test is done on a level part of the green, and stimpmeter readings between 7 and 12 ft are considered acceptable. For a stimpmeter reading of 11.4 ft, what is the coefficient of friction between the ball and the green? (The ball is rolling and not sliding, as we usually assume when considering friction, but this does not change the result in this case.)

diagram in this link :
http://s172.photobucket.com/albums/w30/afghanplayr/?action=view&current=golf.gif

Homework Equations

The Attempt at a Solution

E = K + U + W(work vs. friction )

E = KE + KEi + PE + PEi + uKmgsine(theta)d
since it is at rest initial kinetic and potential are zero

E = 1/2(mv^2) + mgh + uKmgsine(theta)d

KEf = 1/2(0.0459kg)(3.65m/s)^2 = 0.3057 J
PEf = (0.0459)(9.81)(4.2187m) = 1.899 J

Wf= uK(0.0459)(9.81)(sin20)(3.475m)

uK= 1.54

well this is where i realized i was wrong ANY HELPPPPPPPPP I AM REALLY STUCK

Homework Statement

Homework Equations

The Attempt at a Solution

 

[jbsteele]

Use the law of conservation of energy. Let the stimpmeter release height be h and the distance that the ball rolls down the green after the stimpmeter be x. Then the total energy of the system is equal to the change in gravitational potential energy and the work done by friction.E = K + U + W(work vs. friction ) E = KE + KEi + PE + PEi + uKmgsine(theta)dNow, since the ball is rolling without sliding, the only work done is the work done by friction. The initial kinetic energy, initial potential energy, and final kinetic energy are all 0. So, the total energy of the system is equal to the work done by friction:E = uKmgsine(theta)dWhere u is the coefficient of friction between the ball and the green, K is the kinetic energy, m is the mass of the ball, g is the gravitational constant, sine(theta) is the angle of the stimpmeter (20 degrees in this case), and d is the total distance that the ball travels (h + x).Now, we know the total distance that the ball travels (29.3 inches = 0.74572 meters), so we can solve for u:u = E / (Kmgsine(theta)d)u = 0.3057 / (0.0459 * 9.81 * 0.3420 * 0.74572)u = 1.54