physics
posted by rufy
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 on the sphere?

drwls
The speed acquired at the bottom is related to the height of the incline,
H = 3.4 sin 29 = 1.648 m
For a uniformdensity sphere that is not slipping, conservation of energy requires that
(1/2)M V^2 + (1/2)(2/5)V^2 = M g H
V = sqrt(10/7)gH = 4.80 m/s
The acceleration rate (a) of the sphere is such that
V = sqrt(2 a X)
a = V^2/2X = 3.4 m/s^2
The angular acceleration rate is
alpha = a/R = 12.14 radian/s^2
The friction force can now be obtained from the equation relating angular acceleration to torque. The friction force F provides the torque needed to make it spin as it rolls dwn the plank.
F*R = I*alpha = (2/5)MR^2*alpha
F = (2/5)MR*alpha
= (0.4)*3.7 kg*0.18 m*12.14 s^2
= 3.23 N 
rufy
still saying it's wrong
f = N
3.23 NO
HELP: The frictional force provides the torque needed to give an angular acceleration. Therefore, first find the angular acceleration, then apply the rotational equivalent of Newton's 2nd Law (torque = I*a).
HELP: Since the sphere rolls without slipping, the angular acceleration is related to the translational acceleration, which can be found from kinematic relations.
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 121
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 2.7 m down a q = 23° incline. The sphere has a mass M = 4.8 kg and a radius R = 0.28 m. a) Of the total kinetic energy of the sphere, … 
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 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
solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle è = 30o. The sphere has mass M = 8 kg and radius R = 0.19 m . The coefficient of static friction between the sphere and … 
physics
A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle θ = 30o. The sphere has mass M = 8 kg and radius R = 0.19 m . The coefficient of static friction between the sphere … 
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. …