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RATKING
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Homework Statement
An object slides along the ground at speed v at the base of a circular wall of radius r. The object is in contact with both the wall and the ground, and friction acts at both contacts. The wall is vertical and provides no force in the vertical direction. (i) Show that the tangential acceleration of the object is given by dv/dt = −µGg− µWv2/r , where µG and µW are the coefficients of kinetic friction between the object and the ground and wall respectively, and g is the acceleration due to gravity.
Homework Equations
Centripetal Force=(mv2)/r
Frictional Force when moving = coefficient of kinetic friction * Normal force
The Attempt at a Solution
Frictional Force Due to Wall =FW= µW * NW
Normal due to wall is in same direction to centripetal force, these must be equal as the ball doesn't move in this plane and there are no other forces acting here.
Therefore Fc=NW
We know:
Fc=mv2/r
Therefore: mv2/r=NW
Substituting back into equation for Frictional force due to wall:
FW=µW *mv2/r
The frictional force is in the direction tangent to circle.
My problem is that I do not see any other force to be acting tangential, so do not see where a second term comes from.
I say:
Tangential Force =- Frictional Force due to Wall=- µW *mv2/r (as it acts in opposite direction to velocity)
Therefore dv/dt=Tangential Acceleration =- µW *v2/r (Dividing through by m)
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