Physics
posted by Dermot
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 of the sphere
2 what is the total kinetic energy of the ballafter 3s?
3 how far does it roll?
(assume I=(2/5)Mr^2 for a uniform solid sphere.)

drwls
1. Let a be the rate at which the sphere accelerates. After time T from the start of motion, the velocity is
V = a*T and the angular velocity is alpha*T
PE loss equals KE gain.
M g *(1/2)*a T^2*sin 15 = (7/10) M *(a*T)^2
(1/2)a*g*sin15 = (7/10)*a^2
a = (5/7)*g*sin15
The 7/10 comes from adding translational and rotational kinetic energy, using the I value for a solid sphere.
2. Compute V after 3 seconds using the acceleration from part 1. Then compute the total kinetic energy.
3. It rolls to the bottom. Don't you mean how far does it roll in 3 seconds? 
Dermot
yes, sorry after 3 s, thanks.

Damon
constant acceleration a
d = (1/2) a t^2
by the way the angular acceleration alpha = a/R
Respond to this Question
Similar Questions

physics
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 3.4 m down a q = 29° incline. The sphere has a mass M = 3.7 kg and a radius R = 0.28 m. What is the magnitude of the frictional force … 
Physics
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 4.4 m down a q = 20° incline. The sphere has a mass M = 4.6 kg and a radius R = 0.28 m. Of the total kinetic energy of the sphere, what … 
Physics
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 4.4 m down a q = 20° incline. The sphere has a mass M = 4.6 kg and a radius R = 0.28 m. What is the translational kinetic energy of the … 
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
A solid sphere of mass 0.604 kg rolls without slipping along a horizontal surface with a translational speed of 5.25 m/s. It comes to an incline that makes an angle of 38 with the horizontal surface. Neglecting energy losses due to … 
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 uniform solid sphere rolls along a horizontal frictionless surface at 35 m/s and makes a smooth transition onto a frictionless incline having an angle of 300. How far up the incline does the sphere roll when it comes to a momentary … 
Physics
A uniform solid sphere rolls along a horizontal frictionless surface at 35 m/s and makes a smooth transition onto a frictionless incline having an angle of 300. How far up the incline does the sphere roll when it comes to a momentary … 
Physics
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 4.8 m down a θ = 36° incline. The sphere has a mass M = 3.2 kg and a radius R = 0.28 m. If there is no frictional force, what is … 
physics
A solid sphere of radius 35 cm is positioned at the top of an incline that makes 20 ◦ angle with the horizontal. This initial position of the sphere is a vertical distance 3.4 m above its position when at the bottom of the incline. …