Podcast
Questions and Answers
What occurs if the work done by the net force on a particle is negative?
What occurs if the work done by the net force on a particle is negative?
- The particle maintains the same speed.
- The particle slows down. (correct)
- The particle speeds up.
- The particle stops.
Kinetic energy depends linearly on both mass and the direction of motion.
Kinetic energy depends linearly on both mass and the direction of motion.
False (B)
The work-energy theorem states that the network done on a particle equals:
The work-energy theorem states that the network done on a particle equals:
- The particle's total energy.
- The particle's total momentum.
- The change in the particle's potential energy.
- The change in the particle's kinetic energy. (correct)
A tractor pulls a sled loaded with firewood at a constant speed. Considering friction, what is the total work done on the sled?
A tractor pulls a sled loaded with firewood at a constant speed. Considering friction, what is the total work done on the sled?
An elevator is lifted at a constant speed by a steel cable attached to an electric motor. What describes the work done?
An elevator is lifted at a constant speed by a steel cable attached to an electric motor. What describes the work done?
A spring is compressed. What represents the total work done by the force?
A spring is compressed. What represents the total work done by the force?
Gravitational potential energy is dependent on the path taken by the object.
Gravitational potential energy is dependent on the path taken by the object.
If Wtotal = 0 then the ____ does not change and the speed of the particle remains ____.
If Wtotal = 0 then the ____ does not change and the speed of the particle remains ____.
Two iceboats (one of mass $m$, one of mass $2m$ ) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Which iceboat crosses the finish line with greater kinetic energy?
Two iceboats (one of mass $m$, one of mass $2m$ ) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Which iceboat crosses the finish line with greater kinetic energy?
Suppose a car travels up three different roadways from the base of a mountain to the summit. Which path requires the most energy?
Suppose a car travels up three different roadways from the base of a mountain to the summit. Which path requires the most energy?
A block of mass $m$ is released from rest on two frictionless ramps with heights $y_1$ and $y_2$. Which block arrives at the right-hand end with the greater speed?
A block of mass $m$ is released from rest on two frictionless ramps with heights $y_1$ and $y_2$. Which block arrives at the right-hand end with the greater speed?
A block is released from rest on a frictionless incline with a spring at the bottom. What is happening to the gravitational potential energy $U_{grav}$ and the elastic potential energy $U_{el}$?
A block is released from rest on a frictionless incline with a spring at the bottom. What is happening to the gravitational potential energy $U_{grav}$ and the elastic potential energy $U_{el}$?
What term describes a force that allows conversion between kinetic and potential energy?
What term describes a force that allows conversion between kinetic and potential energy?
A force (such as friction) that is not conservative is called a ______ force, or a dissipative force.
A force (such as friction) that is not conservative is called a ______ force, or a dissipative force.
Match the following terms with their descriptions:
Match the following terms with their descriptions:
What is the SI unit of kinetic energy?
What is the SI unit of kinetic energy?
Kinetic energy can be negative if an object is moving in the negative direction.
Kinetic energy can be negative if an object is moving in the negative direction.
How is the product Fs related to work and energy?
How is the product Fs related to work and energy?
The total mechanical energy of a system is defined as:
The total mechanical energy of a system is defined as:
A constant force of 5000 N is applied to a sled at an angle of 36.9 above the horizontal. If the sled, weight, and load are 14,700 N and the friction force is 3500N, what formula equals total work?
A constant force of 5000 N is applied to a sled at an angle of 36.9 above the horizontal. If the sled, weight, and load are 14,700 N and the friction force is 3500N, what formula equals total work?
A woman weighing 600 N steps on to a bathroom scale that contains a heavy spring, compressing it by 1.0 cm. Suppose that the weight of the woman and the displacement of the spring are in the -x direction. What does this tell you?
A woman weighing 600 N steps on to a bathroom scale that contains a heavy spring, compressing it by 1.0 cm. Suppose that the weight of the woman and the displacement of the spring are in the -x direction. What does this tell you?
Suppose a 2000 kg elevator with broken cables is falling at 8.00 m/s. Calculate the force constant of the spring using the expression $E_{total \ mechanical} = K + U_{grav} + U_{el}$ with $K_i + U_i = K_f + U_f$.
Suppose a 2000 kg elevator with broken cables is falling at 8.00 m/s. Calculate the force constant of the spring using the expression $E_{total \ mechanical} = K + U_{grav} + U_{el}$ with $K_i + U_i = K_f + U_f$.
Power is the ______ at which work is done.
Power is the ______ at which work is done.
Two blocks are connected as shown with the rope and pulley are of negligible mass. When released, the block of mass $m_1$ slides down the ramp and the block of mass $m_2$ moves upward. After each block has moved a distance $d$, what can you determine about the total work done on $m_1$
Two blocks are connected as shown with the rope and pulley are of negligible mass. When released, the block of mass $m_1$ slides down the ramp and the block of mass $m_2$ moves upward. After each block has moved a distance $d$, what can you determine about the total work done on $m_1$
Which statement is true regarding conservative forces?
Which statement is true regarding conservative forces?
Mechanical energy is conserved in the presence of non-conservative forces.
Mechanical energy is conserved in the presence of non-conservative forces.
What happens to the mechanical energy for a automobile tire that flexes as it rolls?
What happens to the mechanical energy for a automobile tire that flexes as it rolls?
Match the concepts with its expression
Match the concepts with its expression
If is there is no net force change, what force equation can used used to describe an isolatd system?
If is there is no net force change, what force equation can used used to describe an isolatd system?
Newton's law can be written in terms of momentum: $ \vec{\Sigma F} = lim_{\Delta t \rightarrow 0} \frac{\Delta \vec{P}}{\Delta t}$
Newton's law can be written in terms of momentum: $ \vec{\Sigma F} = lim_{\Delta t \rightarrow 0} \frac{\Delta \vec{P}}{\Delta t}$
Two astronauts push each other as they float freely in the zero-gravity environment of space is a conserved system and has external forces conserved.
Two astronauts push each other as they float freely in the zero-gravity environment of space is a conserved system and has external forces conserved.
A small compact car with a mass of 1000 kg is traveling north, it finds that the total momentum is is 2.5 104 kg m/s at a direction of 36.9. If you wanted to find total momentum, what is the appropriate expression.
A small compact car with a mass of 1000 kg is traveling north, it finds that the total momentum is is 2.5 104 kg m/s at a direction of 36.9. If you wanted to find total momentum, what is the appropriate expression.
What is defined as the Vector sum of the external forces on a system?
What is defined as the Vector sum of the external forces on a system?
What occurs during an elastic collision?
What occurs during an elastic collision?
What properties can change Internal forces on individuals, but can not change the total [blank]of the system;
What properties can change Internal forces on individuals, but can not change the total [blank]of the system;
Mechanical potential equation for vertical coordinate reads: $E_i+mgh+(1/2)Kx^2=E_f$
Mechanical potential equation for vertical coordinate reads: $E_i+mgh+(1/2)Kx^2=E_f$
Determine a one word solution using $s=r theta$ to find linear velocity? Given $v = r w$ and $w= {d \theta} / {dt}$
Determine a one word solution using $s=r theta$ to find linear velocity? Given $v = r w$ and $w= {d \theta} / {dt}$
Internal forces change the ______ of individual particles but not the total momentum of the system.
Internal forces change the ______ of individual particles but not the total momentum of the system.
If the vector sum of the forces on a particle is ____, then the total momentum of the particles do not change.
If the vector sum of the forces on a particle is ____, then the total momentum of the particles do not change.
You are pulling a sled up a hill that has a slope, if there is the addition of friction to the pull, what variable would be used to compensate for the the addition of friction using an equation to described total energy system?
You are pulling a sled up a hill that has a slope, if there is the addition of friction to the pull, what variable would be used to compensate for the the addition of friction using an equation to described total energy system?
Express power in component form: $P = F \vec{r_{.....______}$
Express power in component form: $P = F \vec{r_{.....______}$
Because the gravitational force conservative, the work it does is all the same along all paths.
Because the gravitational force conservative, the work it does is all the same along all paths.
Which exerts more friction that acts within the rubber, Automobile tire or spring?
Which exerts more friction that acts within the rubber, Automobile tire or spring?
Flashcards
Potential Energy
Potential Energy
The energy associated with the position of a system rather than its motion.
Gravitational potential energy
Gravitational potential energy
Vertical coordinate of particle. y increases if particle moves upward.
Gravitational Potential Energy
Gravitational Potential Energy
The quantity, product of the weight mg and the height y above the origin of coordinates.
Gravitational Work
Gravitational Work
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Mechanical Energy
Mechanical Energy
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Conserved Quantity
Conserved Quantity
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Conservation of Energy
Conservation of Energy
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Elasticity
Elasticity
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Elastic potential energy
Elastic potential energy
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Conservative Force
Conservative Force
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Work Done
Work Done
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Non-conservative Force
Non-conservative Force
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Power
Power
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Momentum
Momentum
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Momentum and Newton's Second Law
Momentum and Newton's Second Law
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Zero forces
Zero forces
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Total momentum
Total momentum
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System momentum
System momentum
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Elastic collisions
Elastic collisions
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Total Work
Total Work
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Kinetic Energy
Kinetic Energy
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Study Notes
Work and Energy
- Refers to chapter 7, starting on page 180
- Topics discussed are energy overview, work, kinetic energy, varying force, potential, conservation, non-conservative forces, and power
Work Done by Several Forces
- The total weight of a sled and firewood is 14,700 N
- A tractor pulls the sled 20 m along level ground with a constant force of 5000 N at an angle of 36.9° above the horizontal
- A 3500 N friction force opposes the sled's motion
- The work done by the tractor is 80,000 N·m (80 kJ)
- The work done by friction is -70,000 N·m (-70 kJ)
- The total work done on the sled is the algebraic sum of the work done by each force: Wtot = Ww + Wn + WT + Wf = 0 + 0 + 80 kJ + (-70 kJ) = 10 kJ
Direction of force component
- An elevator moved upwards by a steel cable attached to an electric motor moves at a constant speed
- The Cable does positive work one the elevator, and the elevator will do negative work on the cable
Total Work - Work Energy Theorem
- The work done by the net force on a particle as it moves is called total work
- If Włot > 0, the particle speeds up
- If Włot < 0, the particle slows down
- If Wtot = 0, the particle maintains the same speed
- A particle with mass m under the action of F along the +x-axis has a constant acceleration
- Newton's second law of motion states F=max
- As a particle changes speed from v₁ to v₂, it undergoes a displacement s=x₂-x₁
- Fs = 1/2mv₂ - 1/2mv₁
- Fs is equal to total work
Kinetic Energy
- A kinetic energy particle is in motion
- Kinetic energy is represented by K = ½mv² where:
- m = mass of the particle
- v = speed of the particle
- Kinetic energy is a scalar quantity dependant on the particle's mass and speed, not direction of motion
- Kinetic energy is never negative and it is zero only when a particle is at rest
- SI unit of kinetic energy is the Joule
Kinetic Energy Additional Notes
- Kinetic energy remains the same, regardless of direction of motion
Work-Energy Theorem
- Work energy theorem: Wtot = K2 - K1 = ΔΚ
- Wtot = Total work done on particle
- K2 = Final kinetic energy
- K1 = Initial kinetic energy - ΔΚ = Change in Kinetic energy
- Wtot = Total work done on particle
- During any displacement of the particle, the work done by the net external force on it is equal to its change in kinetic energy
- Although Ks are always positive, W total can be positive, negative or zero
- W total is zero then kinetic energy does not change and the speed of the particle remains constant
Work Done with a Varying Force
- Many forces are not constant
- A particle moving from x₁ to x₂ responds to a changing force in the x-direction
- The total work done by force is represented in a by area under the positions of the curve
Stretching a Spring
- Hooke's law for elongation/compression of a spring: Fspring = kx
- Equal to the area of the shaded triangle/
- Wspring = ½ kx² - ½ kx²
Work Done on a Spring Scale
- A weight on a bathroom spring scale compresess the spring, find force formula for spring
- Formula: Fspring = kx
Gravitational Potential Energy
- Potential energy is the energy associated with the position of a system rather than its motion
- A particle in the gravitational field of Earth has gravitational potential is U grav= mgy
- m = mass of the particle
- g = Acceleration due to gravity
- y = vertical coordinates of particle
- As a basketball descends, gravitational potential energy is converted to kinetic energy
Additional Gravitational Potential Energy Info
- Gravitational potential energy is Ugrav = mgy
- The work done from y₁ to y₂ is Wgrav = Ugrav,i- Ugrav,f = -ΔU grav
- Important to note Wgrav is negative
- Increases with height (∆Ugrav > 0)
- Decreases if the body moves down (∆Ugrav < 0)
Conversion of Mechanical Energy
- Also known as gravitational forces only
- The total mechanical energy of a system is the sum of its kinetic and potential energy
- A quantity that always has the same value is called a conserved quantity.
- W total = [Wconservative = Ui-Uf] = Kf - Ki
- K₁ + U₁ = K₁ + Uf
- ½ mv² + mgy¡ = ½ mv² + mgyf
Extra Notes on Conservation of Mechanical Energy
- Gravity and potential energy only
- moving up
- Velocity decreases, gravitational potential energy increases
- Total Energy = Kinetic energy + Ugrav remains the same
Conservation of Mechanical Energy Example
- Baseball example (0.145KG) throwing at 20.0 m/s straight up, find high how it goes, ignoring air resistance
- After a baseball leaves your hand: E = K+ U conserved
- K₁ + Ugrav,1 = K2 + Ugrav,2
- ½ mv₁² = mgy 2
- Y2 = v1²/2g = (20.0 m/s) 2/(2(9.80 m/s²)) = 20.4 m
Work and Energy Along a Curved Path
- Same expression can be used for gravitational potential energy whether the path is curved or straight
- Work grav = mgy₁-mgy₂
- The total work done by the gravitational force depends on the difference in height between the two points
- Unaffected by a horizontal motion
Elastic Potential Energy
- A body is elastic if it returns to its original shape after being deformed
- Elastic potential energy: Uel = ½ kx²
- k = force constant of spring
- x > 0 if stretched
- x < 0 if compressed
- Achilles acts like a natural spring, reducing workload
Elastic Potential Energy Additional Notes
- A 2000 kg elevator with spring example
- Etotal mechanical = K+Ugrav+Uel = 1/2mv² + mgy+1/2kx²
- So gravitational potential will be Ugrav= U₁ = mgh = 2000 kg × 9.81 m/s² x 3 m
- So springy potential i U₁ = Uel = 1/2 k x2 = 1/2 x k × (-3.00 m)2
- So k = 2.37 × 104 N/m
Nonconservative Forces
- Discusses concept of conservative and nonconservative
- Wother = (Kf+Ugrav,f+Uel,f ) - (Ki+Ugrav,i+Uel,i )
- Conservative forces allow conversion between kinetic and potential energy
- Conservative forces are gravity and spring, nonconservative: friction
Conservative Forces
- The work done by a conservative force depends on the endpoints
Non-Conservative Forces
- Mechanical energy is lost and converted to internal in the tire
- Tire should be checked when cool
Power
- Power is the rate at which work is done
- Average Power during time interval: P avg = ΔW/Δt
- SI unit of power is the watt (1 W = 1 J/s), horsepower (1 hp = 746 W)
- P= lim =- Fv
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