Physics
posted by Joe .
A bowling ball rolls without slipping up a ramp that slopes upward at an angle (beta) to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.
What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable (beta) and appropriate constants.(this was g*sin(beta)/1.4)
What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable (beta) and appropriate constants.
The second part I don't understand how to do. Help is appreciated :/

The equation of motion for a solid sphere rolling uphill is
M*g sinbeta(2/5)M*a = M*a
The second term on the right is the friction force, assuming no slipping.
Rearranging gives you
a = g*sinbeta/1.4
To prevent slipping, the friction force
(2/5)M*a = (2/5)M*g*sinbeta*(5/7)
= (2/7)*M*g*sinbeta must be less than the maximum static friction force
M*g*cosbeta*Us.
Us is the static friction coefficientr.
Slipping starts when the terms on both sides are equal, in which case
Us = (2/7)*tanbeta
Respond to this Question
Similar Questions

Physics
A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the ﬂoor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so ω0 = 0. It picks up rotation due to (kinetic) … 
Physics
A uniform solid sphere of mass 4kg and diameter 20cm initally at rest, begins to roll without slipping under the influece of gravity, down an incline that makes an angle of 15degrees to the horizontal 1 calculate the angular acceleration … 
Physics
After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of v = 3.41 m/s To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h = 0.529 m. What … 
Physics
A uniform solid sphere rolls down an incline without slipping. If the linear acceleration of the center of mass of the sphere is 0.21g, then what is the angle the incline makes with the horizontal? 
physics
After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of v = 3.27 m/s To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h = 0.572 m. What … 
physics
A solid sphere of radius 23 cm is positioned at the top of an incline that makes 23 degree angle with the horizontal. This initial position of the sphere is a vertical distance 3 m above its position when at the bottom of the incline. … 
physics
A spherical bowling ball with mass m = 4.1 kg and radius R = 0.116 m is thrown down the lane with an initial speed of v = 8.9 m/s. The coefficient of kinetic friction between the sliding ball and the ground is ¦Ì = 0.34. Once the … 
Physics
A spherical bowling ball with mass m = 3.2 kg and radius R = 0.107 m is thrown down the lane with an initial speed of v = 8.6 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.34. Once the … 
Physics
After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of = 3.18 m/s. To reach the rack, the ball rolls up a ramp that rises through a vertical distance of = 0.510 m. What … 
Physics
Suppose the height of the ramp is h1= 0.3 m, and the foot of the ramp is horizontal, and is h2= 1.00 m above the floor. What will be the horizontal distance traveled by the following four objects before they hit the floor?