Work energy and power
72 important questions on Work energy and power
What is a scalar quantity?
- Has only magnitude
- No direction
- Example: Work
When does a force perform no work on an object?
- Force perpendicular to displacement.
- No displacement.
- \(\cos 90^\circ = 0\), so work \(W = 0\).
What is the unit of work?
- Joule (J)
- 1 Joule = 1 Newton × 1 meter (1 Nm)
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What is necessary to specify when measuring work on an object?
- Specify which object
- Specify which force
- Specify which distance
What happens when force and displacement are parallel?
- Positive work is done.
- Angle \(\theta = 0^\circ\).
- \(W = F \Delta x \cos 0^\circ\).
How is work calculated when force and displacement are at an angle?
- Work = \( F \cos \theta \Delta x \)
- \( F \) = Force
- \( \Delta x \) = Displacement
- \( \theta \) = Angle between force and displacement
Describe the Law of Conservation of Mechanical Energy.
- Energy can't be created/destroyed.
- Converts from one form to another.
- \(E{pA} + E{kA} = E{pB} + E{kB}\).
What will positive net work do to a system's energy?
- Positive net work will:
- Increase energy of the system.
- Increase speed of the system.
How do you calculate the work done by each force?
- Draw free-body diagram
- Show all forces exerted
- Use: \(W = F \Delta x \cos \theta\)
What is the result when force and displacement are anti-parallel?
- Negative work is done.
- Angle \(\theta = 180^\circ\).
- \(W = F \Delta x \cos 180^\circ\).
What components does applied force \( F \) have?
- Vertical: \( F \sin \theta \)
- Horizontal: \( F \cos \theta \)
- \( F \cos \theta \) does the work
What is the formula for work done when force and displacement are in the same direction?
- Formula: \(W = F \Delta x\).
- \(W\) = work done (Joules).
- \(F\) = force (Newton).
- \(\Delta x\) = displacement (meters).
What is the work-energy theorem?
- Net work done on an object equals change in kinetic energy.
- \( W{\text{net}} = \Delta Ek \)
- \(\Delta Ek = E{kf} - E{ki} \)
- \(\Delta Ek = \frac{1}{2}mvf^2 - \frac{1}{2}mvi^2 \)
What does the angle 30° represent in the calculation?
- Angle of applied force to the floor
- Used in \(\cos \theta\) calculations
Describe the work done when \(\theta\) is acute (< \(90^\circ\)).
- Work is positive.
- Force in same direction as displacement.
- \(0^\circ < \theta < 90^\circ\).
What conditions are needed to perform work on an object?
- Applied force
- Displacement
- Force component parallel to displacement
What are the categories of forces in the conservation of energy principle?
- Conservative forces (Fe):
- Non-wasteful
- Non-conservative forces (Fne):
- Wasteful or external
How does force affect an object's kinetic energy according to the theorem?
- Work by a force increases object's kinetic energy.
- Positive work: \( vf > vi \)
- Negative work: \( vf < vi \)
- Zero work: velocity constant.
What are the acting forces in the free-body diagram?
- Forces:
- Fapplied: Force applied by the man
- f: Frictional force
- w: Truck's weight
- N: Normal force
What is the equation for net work done on the object?
- \(W{\text{net}} = W{F{\text{applied}}} + Wf + Ww + WN\)
Describe the work done when \(\theta\) is obtuse (> \(90^\circ\)).
- Work is negative.
- Force in opposite direction to displacement.
- \(90^\circ < \theta < 180^\circ\).
What can the work done by a force be?
- Positive: if force's component is in the direction of displacement
- Negative: if force's component is opposite
- Zero: if force is perpendicular
What is a non-conservative force?
- Not reversible
- Energy goes to waste
- Example: friction
What happens to work done by a conservative force?
- Stored energy retrievable
- Energy remains unchanged
- Examples: gravity, elastic potential
What is the unit of kinetic energy?
- Measured in joules (J).
What is the mass of the truck in tons and kilograms?
- Mass:
- 3 tons
- 3,000 kg
Describe the steps in Method 2 to calculate net force.
- Draw parallel force diagram
- Calculate net force: \(F{\text{net}} = F{\text{horizontal}} - f\)
- Calculate total work: \(W{\text{net}} = F{\text{net}} \Delta x \cos \theta\)
How does the angle affect work?
- \( \cos 0^\circ \) = 1 (maximum work)
- \( \cos 90^\circ \) = 0 (no work)
- \( \cos 180^\circ \) = -1 (negative work)
What is a conservative force according to Definition 1?
- A conservative force results in zero net work.
- This occurs when the path begins and ends at the same point.
What happens to energy in non-conservative forces?
- Not retrievable
- Energy is lost
- Example: turns into heat
Describe the work done by non-conservative forces.
- Energy not retrievable
- Converted to other forms (e.g., heat)
- Example: friction
What is the acceleration of the truck?
- Acceleration:
- 0.4 m/s²
What forces are considered conservative?
- Conservative forces include:
- Weight (gravitational force)
- No energy loss
- Path-independent
What is a non-conservative force according to Definition 1?
- A non-conservative force results in non-zero net work.
- This occurs when the path starts and ends at the same point.
Describe the work done by gravity along a closed path.
- Work from B to C is zero
- Work from D to A is zero
- Total work is zero
How is work done to lift a container to a height h?
- Work: \( W = F \times \Delta y \)
- \( W = mgh \cos 0^\circ = mgh \)
- Gravity is conservative
What is the equation for net work related to displacement?
- \( W{\text{net}} = F{\text{net}} \Delta x \cos \theta \)
Over what distance is the truck accelerated?
- Distance:
- 5 m
What happens to mechanical energy when non-conservative forces are absent?
- Mechanical energy is conserved.
- \(\Delta Em = 0\)
- \(W{nc} = 0\)
How do non-conservative forces affect work?
- Non-conservative forces:
- Cause path-dependent work
- Include friction
- Can vary energy between points
What is the work done by friction along a closed path?
- Path length: Δd
- Work = -fΔd
- Total work = -4fΔd
How is a roller coaster used to explain conservative forces?
- Ignores frictional forces.
- Cart has same velocity at points with equal height.
- Kinetic energy is zero over complete loop.
What is required to move a container against friction on a floor?
- Work equal to \( Wf \)
- \( F{\text{person}} = F_{\text{person}} \Delta x \cos 180^\circ = -1 \)
- Friction is non-conservative
What is the kinetic frictional force between the truck's wheels and the road?
- Kinetic frictional force:
- 4,000 N
What is power in physics?
- Power indicates how quickly work is done.
- It relates work to time.
- Defined as the rate of work done or energy transferred.
Define the Law of the Conservation of Mechanical Energy.
- Total mechanical energy \((Em)\) is constant.
- \((Ep + E_k) \text{ remains constant}\)
What is the work-energy theorem?
- Total external work change is expressed as:
- \( W{c} = \Delta E{k} + \Delta E_{p} \)
- Uses both kinetic and potential energy
What happens to a roller coaster cart when frictional forces are ignored?
- Same velocity at equal height points A and D.
- Kinetic energy is zero over the entire track.
How does gravity do work on vertical sections of a path?
- Vertical work is positive
- From C to D: Varies
How is power expressed in terms of force and velocity?
- Power \( P \) is calculated with \( P = F \times v{\text{avg}} \)
- \( F \): Constantly applied force (N)
- \( v{\text{avg}} \): Average velocity (m/s)
How is power mathematically expressed?
- Power = Work / Time (P = W / Δt)
- Power = Energy / Time (P = E / Δt)
How is work done by gravitational force calculated when lifted to a height \(\Delta h\)?
- Work formula:
- \( W{c} = W{g} = mg\Delta{h}\cos180^{\circ} \)
- Negative potential energy
What is path dependence for work done by conservative forces?
- Net work done by conservative force on closed paths is zero.
- Work depends on start and end points, not path taken.
State the formula for work done by friction in a specific section.
- Wf = fΔd cos 180°
- Equals -fΔd
What is average power in watts when a 250 kg piano is lifted at 0.1 m/s\(^-1\)?
- Use \( P{\text{avg}} = F \times v{\text{avg}} \)
- \( F = m \times g \)
- \( P_{\text{avg}} = 245\, \text{W} \)
What is the SI unit for power?
- Watt (W)
- 1 watt = 1 joule/second
- 1 W = 1 J/s
What is the effect of conservative forces on mechanical energy?
- Mechanical energy conserved.
- \((Em = Ek + E_p)\) constant
What is the formula for work done by non-conservative forces?
- \( W{nc} = \Delta E{k} + \Delta E_{p} \)
- Change in mechanical energy
How do Definitions 2 of conservative and non-conservative forces differ?
- Conservative: Work depends on start and end point.
- Non-conservative: Work does not depend on the path.
How is the force required for a cyclist moving at 15 m/s on a straight road calculated?
- Forward force \( F = \frac{P}{v{\text{avg}}} \)
- Friction force \( f = F \)
- \( v{\text{avg}} = 15\, \text{m/s} \)
Why was the concept of horsepower introduced?
- Historically used by James Watt.
- To indicate the power of steam engines.
- Horsepower = 745.7 W
Describe what happens to energy in an isolated system with non-conservative forces.
- Mechanical energy not constant.
- Total energy \((Ek, Ep, E_{thermal})\) constant
What is the net work for paths 1 and 2 in the given figure?
- Net work: Wnet = W1 + W2 = 0.
- W1 = -W2 in closed path.
Why doesn't constant speed cycling convert chemical energy to kinetic energy?
- Cyclist moves at constant speed, so net force is zero.
- Energy conversion supports necessary speed only.
How is a car's power often expressed?
- Cars' power is often in horsepower.
- Measures how much work in a given time.
Outline what is meant by mechanical energy not being conserved in real life.
- External forces cause loss.
- Leads to Conservation of Energy principle.
What is the relationship between paths 1 and 3 and their work done?
- Net work: Wnet = W1 + W3 = 0.
- W3 = -W1.
What information is given about Lerato's motion?
- Mass: 60 kg
- Velocity at top: 2 m/s
- Time to top: 2.5 s
How does path 3 differ in terms of its start and end points?
- Path 3 is arbitrary.
- Must start at point B and end at point A.
What is the task for calculating Lerato's power?
- Calculate power to reach top of stairs.
- Use work-energy principles.
What details are provided about Thabo's motion?
- Mass: 80 kg
- Velocity at top: 1.5 m/s
- Time to top: 3 s
What needs to be calculated for Thabo?
- Calculate power to get to the top.
- Use work-energy principles.
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