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Physics Chapter 5 : Topic 4
Work–Energy Theorem in Resistive Media
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The work-energy theorem states that the net work done on an object is equal to:
Reasoning: According to the theorem: $\mathbf{W}_{\mathbf{net}}\mathbf{= \Delta\ }\mathbf{K\ .E}\mathbf{=}\mathbf{K\ .E}_{\mathbf{\ f}}\mathbf{-}\mathbf{K\ .E}_{\mathbf{\ i}}$
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If the net work done on an object is positive, its kinetic energy:
Reasoning: Positive work adds energy to the object.
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The unit of work and kinetic energy is:
Reasoning: Both work and energy are measured in joules.
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According to the work-energy theorem:
Reasoning: Net work causes a change in kinetic energy.
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If the velocity of an object increases, the net work done on it is:
Reasoning: $\mathbf{W}_{\mathbf{net}}\mathbf{=}\mathbf{K\ .E}_{\mathbf{\ f}}\mathbf{-}\mathbf{K\ .E}_{\mathbf{\ i}}$ ; Increasing $\mathbf{K\ .E}$ means positive work.
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A resistive force is a force that:
Reasoning: Resistive forces oppose displacement.
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Which of the following is a resistive force?
Reasoning: Friction opposes motion and dissipates energy.
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In a resistive medium, some mechanical energy is converted into:
Reasoning: Resistance converts mechanical energy into thermal energy.
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When friction acts on a moving object, the work done by friction is:
Reasoning: Friction acts opposite to displacement.
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Air resistance affects a moving object by:
Reasoning: Air resistance removes mechanical energy.
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A block moving on a rough surface slows down because:
Reasoning: Negative work by friction decreases kinetic energy.
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A body has initial kinetic energy of $\mathbf{500\ J}$. Friction does $\mathbf{200\ J}$ negative work. Final kinetic energy is:
Reasoning: $\mathbf{K\ .E}_{\mathbf{\ f}}\mathbf{=}\mathbf{K\ .E}_{\mathbf{\ i}}\mathbf{+ W = 500 - 200 = 300\ J}$
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A car moving on a rough road stops after traveling some distance. The lost kinetic energy is equal to:
Reasoning: Friction removes kinetic energy.
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A$\mathbf{\ }\mathbf{2\ kg}$ object moving at $\mathbf{10\ m/s}$ has kinetic energy:
Reasoning: $\mathbf{K\ .E}\mathbf{=}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}\mathbf{v}^{\mathbf{2}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(2)(100) = 100\ J}$
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If friction removes all kinetic energy of a moving object, the final velocity becomes:
Reasoning: Zero kinetic energy means zero velocity.
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A $\mathbf{5\ kg}$ object moving at $\mathbf{4\ m/s}$ stops due to friction. The work done by friction is:
Reasoning: Initial $\mathbf{K\ .E}$: $\mathbf{K\ .E}\mathbf{=}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(5)(}\mathbf{4}^{\mathbf{2}}\mathbf{) = 40\ J}$Friction removes this energy: $\mathbf{W = - \ 40\ J}$
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A force does $\mathbf{300\ J}$ work on an object initially having $\mathbf{200\ J}$ kinetic energy. Final kinetic energy is:
Reasoning: $\mathbf{K\ .E}_{\mathbf{\ f}}\mathbf{=}\mathbf{K\ .E}_{\mathbf{\ i}}\mathbf{+ W = 200 + 300 =}\mathbf{500\ J}$
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A $\mathbf{1000\ kg}$ car slows from $\mathbf{20\ m/s}$ to $\mathbf{10\ m/s}$ due to resistance. The work done by resistance is:
Reasoning: Resistance reduces kinetic energy.
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A machine does $\mathbf{500\ J}$ work against friction. The energy lost is:
Reasoning: Work against friction equals energy dissipated.
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A ball moving through air slows down because:
Reasoning: Air resistance opposes motion.
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A person pushes a box on a rough floor. The net work done is:
Reasoning: Network includes all forces acting on the object.
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When a car brakes suddenly, the kinetic energy changes into:
Reasoning: Brakes use friction to convert $\mathbf{K\ .E}$ into heat.
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If resistive force increases, the stopping distance of a moving object:
Reasoning: Greater resistance removes kinetic energy faster.
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A parachute slows a falling person because:
Reasoning: Increased drag reduces kinetic energy.
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A body moving with constant speed on a rough horizontal surface has:
Reasoning: Constant speed means constant kinetic energy. $\mathbf{\Longrightarrow}$ $\mathbf{\Delta\ }\mathbf{K\ .E}\mathbf{= 0}$
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A force-displacement graph for resistance is below the displacement axis. The work done is:
Reasoning: Area below axis represents negative work.
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A projectile moving through air has less range than in vacuum because:
Reasoning: Air resistance removes energy from the projectile.
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The total work done on an object in a resistive medium is:
Reasoning: Net work includes every force acting.
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If the net work done on an object is zero, then:
Reasoning: $\mathbf{W}_{\mathbf{net}}\mathbf{= \Delta\ }\mathbf{K\ .E}\mathbf{= 0}$
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A falling object reaches terminal velocity because:
Reasoning: At terminal velocity, net force becomes zero.
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A truck and a car experience the same resistive force. The one with greater kinetic energy will:
Reasoning: More kinetic energy requires more work to stop.
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The work done by friction depends on:
Reasoning: Frictional work: $\mathbf{W = Fs}$
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In a resistive medium, mechanical energy:
Reasoning: Resistance dissipates mechanical energy.
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The work-energy theorem is valid:
Reasoning: It applies to net work by all forces.
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When a moving object stops due to friction, the work done by friction equals:
Reasoning: $\mathbf{W}_{\mathbf{f}}\mathbf{= 0 -}\mathbf{K\ .E}_{\mathbf{\ i}}\mathbf{= - \ }\mathbf{K\ .E}_{\mathbf{\ i}}$
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A force acting opposite to motion causes:
Reasoning: Opposite forces perform negative work.
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