Physics
posted by Jamie
A ball in the shape of a uniform spherical shell (like a soccer ball; I = 2/3 mr2) of mass 1.5 kg and radius 15 cm rolls down a 35 degree incline that is 6.0 m high, measured vertically. The ball starts from rest, and there is enough friction on the incline to prevent slipping of the ball; thus the ball rotates.
a) How fast is the ball moving forward when it reaches the bottom of the incline, and what is its angular speed at that instant?
b) If there were no friction on the incline, how fast would the ball be moving forward and what would be its angular speed at the bottom?
I think I have a lot of b... Can you please check what I have so far and help me with what I'm getting wrong? I have to get all parts of this question correct to get any credit at all so I would appreciate any direction. Thanks!
For a)
F(incline) = mgsinθ = (1.5)(9.8)(sin35) = 8.43 N
x=6/sin35 ==> x = 10.46 (hypotenuse of incline)
I'm not sure where to go from here...
For b) I have:
(kinetic)i + (gravitational)i = (kinetic)f + (gravitational)f... so,
1/2mv^2 + mgy = 1/2 mv^2 + mgy (initial v=0, final y=0), so...
mgy = 1/2mv^2
v^2 = 2gy
v = sqrt(2gy) ==> sqrt(2(9.8)(6)) = 10.8 m/s = v
Then, to find angular speed,
w=v/r
w= 10.8 (m/s)/15 = 0.72
Then K(rot) = 1/2Iw^2
1/2(2/3(1.5)(15^2))(72^2) = 58.32 angular speed, but I know this isn't right. What did I do wrong?

John
oh nah lmao
Respond to this Question
Similar Questions

Physics HELP!!!
A ball (radius 0.2 m) is rolling on level ground toward an incline. If its velocity is 3 m/s, to what maximum height above the ground does it roll up the incline? 
physics
A ball of mass .15 kg and a radius of .24 m is at the top of a 3.5 m tall hill with a 25 degree incline. What is the velocity of the ball as it reaches the bottom of the hill if it (a) rolls without slipping? 
Physics
A cylinder ( I = 1/2 MR2), a sphere ( I = 2/5 MR2), and a hoop ( I = MR2) roll without slipping down the same incline, beginning from rest at the same height. All three objects share the same radius and total mass. Which object … 
Physics
The moment of inertia of a solid uniform sphere of mass M and radius R is given by the equation I=(2/5)MR2 . Such a sphere is released from rest at the top of an inclined plane of height h, length L, and incline angle è. If the sphere … 
physics
A solid ball of radius b and mass m is released from the top of an incline of the incline is at the height h above the ground. If the ball rolls without slipping, what willl be its linear speed when it reaches the botton of the incline? 
mechanics and heat
A tennis ball of mass m and radius R = 3 cm rolls up without slipping an inclined plane of inclination angle of 37 degree as shown in the figure at the bottom of the incline the center of mass velocity of the ball is v = 10 m/s . The … 
physics 201
A soccer ball is released from the top of a smooth incline. After 3.90 s the ball travels 10.0 m. One second later it has reached the bottom of the incline. Assume the ball's acceleration is constant and determine its value ( m/s2). … 
AP Physics
A 25 degree incline sits on a 1.2 meter high table. a ball rolls off the incline with a velocity of 4 m/s. how far does the ball travel across the room before reaching the floor? 
physics
A soccer ball is released from the top of a smooth incline. After 4.54 s the ball travels 8.1 m. One second later it has reached the bottom of the incline. Assume the ball's acceleration is constant and determine its value ( m/s2). … 
Physics
A tennis ball, starting from rest at a height h = 2.10 m, rolls down the hill. At the end of the hill the ball becomes airborne, leaving at an angle of 27.0° with respect to the ground. Treat the ball as a thinwalled spherical shell …