Question

Use energy methods to determine the final speed of a vacuum cleaner that is pulled 1.5m...

Use energy methods to determine the final speed of a vacuum cleaner that is pulled 1.5m across the carpet with a 19N force at an angle 42 degrees above the horizontal. The vacuum cleaner starts from rest, has a mass of 5.7kg and there is a frictional force of 12N acting.

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Answer #1

Mass of the vacuum cleaner = m = 5.7 kg

Force with which the vacuum cleaner is pulled = F = 19 N

Angle at which the force is applied = = 42o above the horizontal

Horizontal force on the vacuum cleaner = Fx = FCos = (19)Cos(42) = 14.12 N

Frictional force acting on the vacuum cleaner = f = 12 N

Distance the vacuum cleaner is pulled = L = 1.5 m

Initial speed of the vacuum cleaner = V1 = 0 m/s (At rest)

Final speed of the vacuum cleaner = V2

The work done by the force with which the vacuum cleaner is pulled is equal to the change in kinetic energy of the vacuum cleaner plus the work done against friction.

FxL = mV22/2 - mV12/2 + fL

(14.12)(1.5) = (5.7)V22/2 - (5.7)(0)2/2 + (12)(1.5)

V2 = 1.06 m/s

Final speed of the vacuum cleaner = 1.06 m/s

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