A 0.04KG BEAD SLIDES ON A CURVED STARTING FROM REST AT POINT A.THE EARTH FROM A AND B IS FRICTIONLESS ,WHILST THE PATH FROM B TO C IS ROUGH.IF THE BEAD ARRIVES AT POINT C WITH A SPEED OF 1M/S DERTIMINETHE AMOUNT OF WORKDONE BY THE FRICTIONAL FORCE IN PASSING FROM B TO C?
Additional information is required on the elevation drop from A to C. Call it H.
The work done BY friction will be MINUS the difference between potential energy loss and kinetic energy gain
= M [gH - V^2/2)]
To determine the amount of work done by the frictional force in passing from point B to C, we need to calculate the change in kinetic energy of the bead.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = ΔKE
In this case, the bead starts from rest at point A, so its initial kinetic energy (KE1) is zero. The final kinetic energy (KE2) at point C is given by:
KE2 = 1/2 * m * v^2
Where:
m = mass of the bead = 0.04 kg
v = speed of the bead at point C = 1 m/s
Substituting the given values into the equation, we can calculate KE2:
KE2 = 1/2 * 0.04 kg * (1 m/s)^2
= 0.02 Joules
Now, since the frictional force acts in the opposite direction of motion, it does negative work on the bead. Therefore, the work done by the frictional force (W) is equal to the negative change in kinetic energy:
W = -ΔKE = - (KE2 - KE1)
= - (0.02 J - 0 J)
= -0.02 J
Therefore, the amount of work done by the frictional force in passing from point B to C is -0.02 Joules (or 0.02 Joules of work done against the frictional force).
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