- #1
kudoushinichi88
- 129
- 2
This problem is part of a main problem...
A can is placed on a block of mass m which in turn is initially at
rest on a horizontal frictionless table. If a horizontal force F is applied to
the block, it accelerates and the cylinder rolls without slipping. Find the
linear accelerations of the block and the can with respect to the table, and the
angular acceleration of the can about its centre of mass.
[tex]\tau=Fr=I\alpha[/tex]
linear acceleration of the block
[tex]a_{block}=\frac{F}{M+m}[/tex]
linear acceleration of the can
[tex]a_{can}=0[/tex] (it is stationary with respect to the table since it is rolling without slipping)
angular acceleration of the can
from the previous part of the question, the moment of inertia of the can is
[tex]I=\frac{3}{4}MR^2[/tex]
The torque is produced by the frictional force acting on the can, which equal to F. So,
[tex]FR=\frac{3}{4}MR^2\alpha[/tex]
which leads to
[tex]\alpha=\frac{4F}{3MR}[/tex]
Am I missing something?
Homework Statement
A can is placed on a block of mass m which in turn is initially at
rest on a horizontal frictionless table. If a horizontal force F is applied to
the block, it accelerates and the cylinder rolls without slipping. Find the
linear accelerations of the block and the can with respect to the table, and the
angular acceleration of the can about its centre of mass.
Homework Equations
[tex]\tau=Fr=I\alpha[/tex]
The Attempt at a Solution
linear acceleration of the block
[tex]a_{block}=\frac{F}{M+m}[/tex]
linear acceleration of the can
[tex]a_{can}=0[/tex] (it is stationary with respect to the table since it is rolling without slipping)
angular acceleration of the can
from the previous part of the question, the moment of inertia of the can is
[tex]I=\frac{3}{4}MR^2[/tex]
The torque is produced by the frictional force acting on the can, which equal to F. So,
[tex]FR=\frac{3}{4}MR^2\alpha[/tex]
which leads to
[tex]\alpha=\frac{4F}{3MR}[/tex]
Am I missing something?