Answer:
Explanation:
We can use the work-energy principle to find the work done by the applied force to stop the disk. The work-energy principle states that the work done by all forces acting on an object is equal to the change in its kinetic energy:
W = ΔK
where W is the work done, and ΔK is the change in kinetic energy.
Initially, the disk is rotating with an angular velocity of 950 rev/min. We need to convert this to radians per second, which gives:
ω_initial = (950 rev/min) × (2π rad/rev) × (1 min/60 s) = 99.23 rad/s
The initial kinetic energy of the disk is:
K_initial = (1/2) I ω_initial^2
where I is the moment of inertia of the disk about its axis of rotation. For a uniform disk, the moment of inertia is:
I = (1/2) m R^2
where m is the mass of the disk, and R is the radius. Substituting the given values, we get:
I = (1/2) (190 kg) (1.1 m)^2 = 115.5 kg m^2
Therefore, the initial kinetic energy of the disk is:
K_initial = (1/2) (115.5 kg m^2) (99.23 rad/s)^2 = 565201 J
To stop the disk, the applied force must act opposite to the direction of motion of the disk, and must cause a negative change in the kinetic energy of the disk. The force is applied at a radial distance of 0.5 m, which gives a torque of:
τ = F r
where F is the magnitude of the force. The torque causes a negative change in the angular velocity of the disk, given by:
Δω = τ / I
The work done by the applied force is:
W = ΔK = - (1/2) I Δω^2
Substituting the given values, we get:
W = - (1/2) (115.5 kg m^2) [(F r) / I]^2
The force F can be eliminated using the equation for torque:
F = τ / r = (Δω) I / r
Substituting this into the equation for work, we get:
W = - (1/2) (115.5 kg m^2) [(Δω) I / r I]^2
= - (1/2) (115.5 kg m^2) (Δω / r)^2
Substituting the values for Δω and r, we get:
W = - (1/2) (115.5 kg m^2) [(F r / I) / r]^2
= - (1/2) (115.5 kg m^2) [(2 Δω / R) / (2/5 m R^2)]^2
= - (1/2) (115.5 kg m^2) (25/4) (2 Δω / R)^2
= - 90609 J
where we have used the expression for the moment of inertia of a uniform disk and the given values for the mass and radius. The negative sign indicates that the work done by the applied force is negative, which means that the force does negative work (i.e., it takes energy away from the system). The work done by the force to stop the disk is therefore 90609 J, which is -90.6 kJ (to two decimal places).
A metal wire, fixed at one end, has length l and cross-sectional area A. The wire extends a distance e which mass m is hung from the other end of the wire.What is an expression for the Young Modulus E of the metal?
The expression for the Young Modulus E of the metal is E = mgl / Ae. The Young Modulus E of the metal is calculated using the equation E = (F l) / (A e2 m), where F is the force applied to the wire.
To find the expression for the Young modulus E of a metal wire with length l, cross-sectional area A, and mass m hung from the other end of the wire, we need to use the following formula:Stress (σ) = Load (F) / Area (A)Strain (ε) = Extension (Δl) / Original length (l)Young Modulus (E) = Stress (σ) / Strain (ε)We know that the metal wire is fixed at one end and the wire extends a distance e when a mass m is hung from the other end of the wire. Therefore, the extension Δl is equal to e.
Let's assume that g is the acceleration due to gravity. Therefore, the load F is equal to m * g.Substituting the values of F, A, and Δl in the above formula, we get:Stress (σ) = F / A = (m * g) / AStrain (ε) = Δl / l = e / lYoung Modulus (E) = Stress (σ) / Strain (ε)= (m * g) / (A * e / l) = mgl / AeTherefore, an expression for the Young Modulus E of the metal is E = mgl / Ae.
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In this circuit, what is the potential difference across C4?
Use the following values in your calculation:
V = 12.0 V
C1 = 3.0 ?F
C2 = 2.0 ?F
C3 = 2.0?F
C4 = 1.0 ?F
C5 = 4.0 ?F
V4 =
The potential difference across C4 can be found using the equation V = V4 - V3. Using the given values, V = 12.0V, C1 = 3.0 ?F, C2 = 2.0 ?F, C3 = 2.0 ?F, C4 = 1.0 ?F, and C5 = 4.0 ?F, we can solve for V4.
V4 = 12.0V + (3.0 ?F + 2.0 ?F + 2.0 ?F + 1.0 ?F) / (1.0 ?F + 4.0 ?F)
V4 = 12.0V + (8.0 ?F / 5.0 ?F)
V4 = 12.0V + 1.6V
V4 = 13.6V
Therefore, the potential difference across C4 is 13.6V - 12.0V = 1.6V.
The potential difference across C4 can be determined using the formula Q = CV. Where Q represents the charge stored in the capacitor, C represents capacitance, and V represents the potential difference across the capacitorTo determine the potential difference across C4, we can use the formula Q = CV. To determine Q, we need to determine the equivalent capacitance of the circuit.
The equivalent capacitance of capacitors in parallel is equal to the sum of their capacitance. The equivalent capacitance of capacitors in series is equal to the reciprocal of the sum of their reciprocals.C1, C2, and C3 are in series, and their equivalent capacitance is given by:C_eq1=1/((1/C1)+(1/C2)+(1/C3))=1/(1/3+1/2+1/2)=3/7 μF{C_eq1=1/((1/C1)+(1/C2)+(1/C3))=1/(1/3+1/2+1/2)=3/7μF}C_eq2 is the equivalent capacitance of C4 and C5 in parallel.C_eq2=C4+C5=1+4=5μF {C_eq2=C4+C5=1+4=5μF}
Now we can determine the equivalent capacitance of the entire circuit.C_eq=C_eq1+C_eq2=3/7+5=38/7μF{C_eq=C_eq1+C_eq2=3/7+5=38/7μF}Now, we can determine the charge stored in the circuit.Q=C_eqV=38/7*12= 65.14μC{Q=C_eqV=38/7*12=65.14μC}To determine the potential difference across C4, we can use the formula Q = CV.V=C4Q/C4= 65.14/1 = 65.14V{V=C4Q/C4=65.14/1=65.14V}Therefore, the potential difference across C4 is 65.14 V.
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Two pieces of clay, one white and one gray, are thrown through the air. The
m
white clay has a momentum of 25 kg, and the gray clay has a
S
momentum of -30 kg immediately before they collide.
What is the magnitude and direction of their final momentum immediately
after the collision?
Your answer should have one significant figure.
h
kg.
m
-
m
S
S
we can't give a specific direction for the final momentum.
What is momentum?
Momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity. Mathematically, momentum is expressed as:
Momentum (p) = mass (m) x velocity (v)
p = m x v
To solve this problem, we need to apply the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it.
The initial total momentum of the system is:
p_initial = p_white + p_gray = 25 kg m/s - 30 kg m/s = -5 kg m/s
Since there are no external forces acting on the system, the total momentum of the system after the collision must also be -5 kg m/s. Therefore, the final momentum of the system is:
p_final = -5 kg m/s
The direction of the final momentum can be found by looking at the directions of the initial momenta. Since the white clay has positive momentum and the gray clay has negative momentum, we can say that the white clay is moving to the right and the gray clay is moving to the left before the collision.
During the collision, the two clays will exert forces on each other, causing them to change direction and possibly even break apart. Without more information about the collision, we can't say for sure what the direction of the final momentum will be. It could be to the left or to the right, or some combination of the two. Therefore, we can't give a specific direction for the final momentum.
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Estimat the number and wattage of lamps. which would be required to illuminate a workshop space 60x1.5 meteres by means of lamps mounted 5 metres above the working Plane The average illumination required is about 100 wt. coefficient of utilisation = 0.4 luminous efficiency 16 lumens per watt. Assume a space-height ratio of unity and a cundle Power depreciation of 20%
The number and wattage of lamps required to illuminate the workshop would be approximately 8 lamps and 70 watts respectively.
Wattage calculationTo estimate the number and wattage of lamps required to illuminate a workshop space of 60x1.5 meters, we can follow these steps:
Calculate the area of the workshop:
Area = length x widthArea = 60m x 1.5mArea = 90 square metersDetermine the total lumens required:
Lumens = area x average illuminationLumens = 90 sq m x 100 luxLumens = 9000 lumensAdjust for the coefficient of utilization and luminous efficiency:
Effective lumens = lumens / (coefficient of utilization x luminous efficiency)Effective lumens = 9000 / (0.4 x 16)Effective lumens = 1406.25 lumensAdjust for space-height ratio and candle power depreciation:
Effective lumens per lamp = effective lumens x space-height ratio x (1 - depreciation)Effective lumens per lamp = 1406.25 x 1 x (1 - 0.2)Effective lumens per lamp = 1125 lumensDetermine the number of lamps required:
Number of lamps = total lumens required / effective lumens per lampNumber of lamps = 9000 / 1125Number of lamps = 8 lamps (rounded up)Determine the wattage of each lamp:
Wattage per lamp = effective lumens per lamp / luminous efficiencyWattage per lamp = 1125 / 16Wattage per lamp = 70.3 watts (rounded up)Therefore, approximately 8 lamps with a wattage of 70 watts each would be required to illuminate the workshop space.
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Two long parallel wires placed side by side on a horizontal table carry the same currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. Determine the direction of the magnetic field at the point exactly midway between the two wires from your point of view. Explain your answer with the aid of labelled diagram. [5 marked
To find:-
Magnetic field at the centre between the wires.Answer:-
We are here given that two long current carrying wires are having same current. We need to find out the magnetic field at the centre between the wires .
We know that for a point between two ends of a wire , magnetic field is given by,
[tex]\implies B =\dfrac{\mu_0}{4\pi}\dfrac{2i}{d}\\[/tex]
where ,
B is magnetic field.i is the current.d is the distance .Now since magnetic field is a vector quantity we need to find out the direction of the field . We can do so by using Right Hand thumb rule .
Right hand thumb rule :-
Hold the wire , in your hand with thumbs towards the direction of the current, then the curling of the fingers would give you the direction of the magnetic field.
For wire AB :-
The direction comes to be down the page .
For wire CD :-
The direction comes to be down the page .
Calculating net magnetic field:-
The net magnetic field will be the sum of both the fields .
[tex]\implies B_{net}=\dfrac{\mu_0}{4\pi}\dfrac{2i}{d}+\dfrac{\mu_0}{4\pi}\dfrac{2i}{d} \\[/tex]
[tex]\implies B_{net}=\dfrac{\mu_0}{4\pi}\dfrac{4i}{d}\\[/tex]
[tex]\implies \underline{\underline{\green{ B_{net}=\dfrac{\mu_0i}{ \pi d}}}}\\[/tex]
The direction is down the page .
and we are done!
For small bodies with high thermal conductivity, the features surrounding the medium that favor lumped system analysis
The medium should be a poor conductor of heat
The medium should be motionless
Small bodies with high thermal conductivity, the medium should be a poor conductor of heat and should be motionless in order to favour lumped system analysis.
For small bodies with high thermal conductivity, the features surrounding the medium that favor lumped system analysis are that the medium should be a poor conductor of heat and the medium should be motionless.
In other words, for small bodies with high thermal conductivity, the thermal energy will stay confined within the boundaries of the medium if it is a poor conductor of heat and the medium is not moving. This allows the energy to be spread evenly throughout the system, which is why lumped system analysis can be used.
Lumped system analysis is a method used to analyse heat transfer and energy flow within a system. It assumes that thermal energy is transferred across a body of homogeneous material and can be used to calculate the temperature of an object at different points in the body.
The effectiveness of this method relies on the heat capacity of the medium and its thermal conductivity, which is why it is most suitable for small bodies with high thermal conductivity.
For large bodies, or bodies with low thermal conductivity, distributed system analysis is typically used instead of lumped system analysis. This method assumes that the body has different thermal properties at different points, and calculates the temperature at those points based on their respective thermal properties.
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125cm³ of a gas was collected at 15 °C and 755 mm of mercury pressure. Calculate the volume of the gas that will be collected at standard temperature and pressure
Answer:
119,2 см³
Explanation:
по формуле Клопейрона (P1×V1):T1=(P2×V2):T2
если из этой формулы найти V2, ответ будет равен примерно на 119,2 см³
Find the equivalent resistance of the combination shown in Figure 4, assuming that
R5 = 17 Ω and R6 = 26 Ω.
Answer:
Explanation:
R/^5*r^6 Ok so then this is simple once u get the answer u need to use the given formula in order to plug in the numbres sorry .
So basically
12 x r^6(u must fill in the number s ) and then u need to do `13x14xr the answer and use the rest of the numbers in order to figure out the quantities of each side for the shape . Then ur answer would be the r^x + x = ???
So yeah hope this helped
I think
Kind of
K Thanks Bye
A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 x 10â€"27 kg and e = 1.6 x 10â€"19 C
Which ion falls at position 2?
At position 2, ion B falls. It is less deflected because it has a lesser mass than ions C, D, and E and the same charge as ion A.
A force perpendicular to the charged particle's velocity and the magnetic field's direction is applied when it reaches the magnetic field. The right-hand rule asserts that the palm will face the direction of the force if the thumb of the right hand points in the direction of the particle's velocity and the fingers point in the direction of the magnetic field. The particle's charge, velocity, and magnetic field intensity all affect how much force is generated.
Since all ions are moving at the same speed in this scenario, the force exerted on each ion is proportional to its charge to mass ratio. Ion B has the smallest mass of all the ions, so the least force and is least deflected of the ions, falling at position 2.
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Commercially available large wind turbines blade span diameters larger than 100 m and over 3 MW of electric power at peak design have generate conditions. Consider a wind turbine with a 75-m blade span subjected to 25-km/h steady winds. If the combined turbine–generator effi- ciency of the wind turbine is 32 percent, determine (a) the power generated by the turbine and (b) the horizontal force exerted by the wind on the supporting mast of the turbine. Take the density of air to be 1.25 kg/m3, and disregard frictional effects on the mast.
The horizontal force that was exerted by the wind on the mast based on the power is 67.3KN.
What is the force?Blade Stan, d = 75m
Radius of Blade, r = 75m
wind velocity, V = 30 km/h V = 8.333 m/s
Turbine Generator efficiency or Power Co-efficient ((p) = 32% 0.32.
Flow rate across the turbine (in) = 125X8.333X X (75) 2 m
= 46017.583 kg/s
Air Exit velocity, Ve = V×√1 - Nterbine
Ve = 8.333 x √1 1- 0.32
Ve = 6.872 mls
Horizental force in x-direction (F); -
Fx = m (ve-v)
Fx = 46017-583X(6-872-8.333) = 67265.381 N
The Horizental force Extered on the Supporting mast F = -F F= 67.2654 KN
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Determine the horizontal force that was exerted by the wind on the mast base
23.____ are pieces of metal that are temporarily attached to the weldment’s parts to enable them to be forced intoplace. Anytime these pieces of metals are used, they must be removed and the area ground smooth.a.Hammersc.Jacksb.Anvilsd.Cleats or dogs
Cleats or dogs are pieces of metal that are temporarily attached to the weldment’s parts to enable them to be forced into place. Anytime these pieces of metal are used, they must be removed, and the area around Smooth
In this case option D
Cleats or dogs are pieces of metal that are commonly used in welding to temporarily attach the parts of the weldment in place. They are typically small metal pieces with angled ends that can be clamped or welded onto the parts being joined to hold them in the correct position during the welding process.
Once the welding is completed, the cleats or dogs must be removed and the area where they were attached must be ground smooth.
This ensures that the final welded joint has a smooth and even surface and that there are no residual metal pieces that could interfere with the joint's structural integrity.
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an electron is moving parallel to an electric field (from higher to lower voltage). its potential energy is
The potential energy of an electron moving parallel to an electric field decreases as it moves from higher voltage to lower voltage. The work done by the electric field on the electron is equal to the decrease in potential energy. The potential energy of the electron is proportional to its charge and the voltage difference between the two points.
When an electron moves parallel to an electric field, its potential energy is conserved. The potential energy of an electron is proportional to its charge and the voltage through which it moves. As the electron moves from higher voltage to a lower voltage, its potential energy decreases. The work done by the electric field on the electron is equal to the decrease in potential energy. When the electron is at rest, it has a certain potential energy due to its position in the electric field. If the electron is allowed to move freely, it will accelerate towards the lower voltage region, gaining kinetic energy. As it moves, the electric field continues to do work on the electron, converting its potential energy into kinetic energy. If the electric field is uniform, the potential energy of the electron will be given by the equation U = -qV, where q is the charge of the electron and V is the voltage difference between the two points. The negative sign indicates that the potential energy decreases as the voltage difference decreases.
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3. Large amplitude vibrations produced when the of receiver of the applied forced vibration matches the
An object's amplitude dramatically increases when the frequency of the applied forced vibrations matches the object's natural frequency. Resonance describes this behavior.
Theory A wave's amplitude directly relates to the quantity of energy it can carry. A wave with a high amplitude carries a lot of energy, whereas one with a low amplitude carries only a little. A wave's strength is determined by the typical energy that moves through a given area in a certain amount of time and in a particular direction.The sound wave's amplitude grows in proportion to its strength. We perceive louder noises to be of higher intensity. Comparative sound intensities are frequently expressed using decibels (dB)For more information on amplitude of vibration kindly visit to
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Determine the linear velocity of blood in the aorta with a radis of 1.5 cm, if the duration of systole is 0.25 s, the stroke volume is 60 ml.
Answer:
The linear velocity of blood in the aorta can be calculated using the equation:
v = Q / A
where v is the linear velocity, Q is the volume flow rate, and A is the cross-sectional area of the vessel.
The volume flow rate Q can be calculated using the equation:
Q = SV / t
where SV is the stroke volume and t is the duration of systole.
The cross-sectional area of the aorta can be calculated using the equation:
A = πr^2
where r is the radius of the aorta.
Given that the radius of the aorta is 1.5 cm, the stroke volume is 60 ml, and the duration of systole is 0.25 s, we can calculate the volume flow rate Q:
Q = SV / t = 60 ml / 0.25 s = 240 ml/s
Converting the units of Q to cm^3/s:
Q = 240 ml/s × 1 cm^3/1 ml = 240 cm^3/s
We can then calculate the cross-sectional area of the aorta:
A = πr^2 = π × (1.5 cm)^2 = 7.07 cm^2
Finally, we can calculate the linear velocity of blood in the aorta:
v = Q / A = 240 cm^3/s / 7.07 cm^2 = 33.9 cm/s
Therefore, the linear velocity of blood in the aorta is 33.9 cm/s.
Which one of the following types of electromagnetic radiation is produced by the sudden deceleration of high speed electrons?
a.x-rays
b.microwaves
c.infrared radiation
d.visible light
e.gamma rays
The correct answer is a. x-rays is produced by the sudden deceleration of high speed electrons.
What is x-rays?
When high-speed electrons are suddenly decelerated or slowed down, they release energy in the form of electromagnetic radiation. This process is known as bremsstrahlung or "braking radiation". The energy of the emitted radiation depends on the initial speed of the electrons and the degree of deceleration.
In the case of bremsstrahlung, the emitted radiation can range from radio waves to gamma rays, but the highest energy radiation produced by bremsstrahlung is x-rays. Therefore, the sudden deceleration of high-speed electrons produces x-rays.
X-rays are ionizing radiation, meaning that they have enough energy to remove electrons from atoms or molecules, which can cause damage to living tissue. Therefore, exposure to X-rays should be limited and controlled to minimize health risks.
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Complete question is: x-rays is produced by the sudden deceleration of high speed electrons.
imagine that the blue light and orange light from the source were blocked. what color would how be present in the spectrum of light observed
Everything but blue & orange would now be present in the spectrum of light observed.
Spectrum refers to a range of different wavelengths of electromagnetic radiation. Electromagnetic radiation is a form of energy that travels through space and includes different types such as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Each type of electromagnetic radiation has a different wavelength and frequency, and together they make up the electromagnetic spectrum.
The concept of spectrum is used in a variety of fields, including physics, astronomy, and telecommunications. The spectrum of electromagnetic radiation is essential for many technologies, such as radios and televisions, cell phones, and medical imaging devices, as they all rely on the transmission and reception of specific wavelengths of electromagnetic radiation.
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Complete Question: -
Imagine that the blue light and orange light from the source were blocked. What color(s) would now be present in the spectrum of light observed?
Adult brains are not capable of neurogenesiss . True False
Answer:
False. Adult brains are capable of neurogenesis, which is the process of generating new neurons (nerve cells) in the brain. Although it was previously believed that neurogenesis only occurred during early development, research has shown that certain regions of the brain, such as the hippocampus, continue to produce new neurons throughout adulthood. However, the rate of neurogenesis in adults is much lower than in developing brains
EX :SOMEONE FATHER TODAY YOUR FATHER DOES,T KNOW ABOUT TECH OR ANY SAMRT APPS BUT HE KNOW BETTER N HIS GENRATON
The beat frequency produced when a 240 hertz tuning fork and a 246 hertz tuning fork are sounded together is
a) 245 hertz
b) 240 hertz
c) 12 hertz
d) 6 hertz
e) none of the above
The beat frequency produced when a 240-hertz tuning fork and a 246-hertz tuning fork are sounded together would be 6 hertz. Option D.
Frequency combinationThe beat frequency produced when two tuning forks are sounded together is equal to the absolute value of the difference between their frequencies.
In this case, the beat frequency is:
|240 Hz - 246 Hz| = |-6 Hz| = 6 Hz
Therefore, the answer is (d) 6 hertz.
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Find the acceleration vector for the charge. Enter the x, y, and z components of the acceleration in meters per second squared separated by commas. A= m/s^2 To practice Problem-Solving Strategy 27.1: Magnetic Forces. A particle with mass 1.81 xio-3 kg and a charge of 1.22 times sign 10^-8 C has, at a given instant, a velocity v = (3.00 times sign 10^4 m/s)j. What are the magnitude and direction of the particle's acceleration produced by a uniform magnetic field B=(1.63 T)i+(0.980 T)j? Draw the velocity v and magnetic field B vectors. Since they have different units, their relative magnitudes aren't relevant. Be certain they have the correct orientations relative to the given coordinate system. The dot in the center of the image represents the particle. Recall that i, j, and k are the unit vectors in the x, y, and z directions, respectively
The x, y, and z components of the acceleration are -3.17 x 10^2 m/s^2, -3.17 x 10^2 m/s^2, and -3.17 x 10^-1 m/s^2, respectively.
What is Acceleration?
Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction. When an object undergoes acceleration, its velocity changes either in magnitude, direction, or both. The formula for acceleration is a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is the time taken for the change in velocity.
Using the formula for the magnetic force on a moving charged particle, F = q(v x B), we can find the acceleration vector by dividing the force by the mass of the particle, a = F/m.
The velocity vector v = (0, 3.00 x 10^4, 0) m/s has only a y-component, and the magnetic field vector B = (1.63, 0.980, 0) T has only x- and y-components. Therefore, the cross product of v and B only has a z-component:
v x B = (3.00 x 10^4)i x 0.980j - (3.00 x 10^4)j x 1.63i = -4.71 x 10^7 k m/s
The magnetic force on the charge is then given by:
F = q(v x B) = (1.22 x 10^-8 C)(-4.71 x 10^7 k m/s) = -5.74 x 10^-1 N k
Finally, the acceleration vector is:
a = F/m = (-5.74 x 10^-1 N k)/(1.81 x 10^-3 kg) = (-3.17 x 10^2 i - 3.17 x 10^2 j - 3.17 x 10^-1 k) m/s^2
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I need some help with this problem
Tensile force refers to the stretching forces that operate on a substance and consists of two components: tensile tension and tensile strain. This indicates that the substance being acted upon is under tension, and the forces are attempting to stretch it.
What Does Tensile Force Mean?Tensile force refers to the stretching forces that operate on a substance and consists of two components: tensile tension and tensile strain. This indicates that the substance being acted upon is under tension, and the forces are attempting to stretch it.
When a tensile force is applied to a substance, a stress equivalent to the applied force forms, contracting the cross-section and elongating the length.
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Use the work energy theorem to rank the final kinetic energy of a ball based on the initial kinetic energy Ki, the magnitude of a constant force F on the ball, the displacement of the ball, d and the angle, theta between the displacement of the ball and the net force on the ball. Rank from greatest kinetic energy (1) to least kinetic energy (4).
a) Ki=150J F=10N d=15m theta=90 degrees
b) Ki=300J F=200N d=1.5m theta=180 degrees
c) Ki=200J F=25N d=4m theta=0 degrees
d) Ki=450J F=15N d=30m theta=150 degrees
Answer:
Explanation:
The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Therefore, we can use this theorem to calculate the final kinetic energy of the ball in each case.
We know that the work done by a constant force is given by the equation W = Fd cos(theta), where F is the magnitude of the force, d is the displacement of the ball, and theta is the angle between the force and displacement vectors.
Using the work-energy theorem, we can write:
W = ΔK = Kf - Ki
where ΔK is the change in kinetic energy, Kf is the final kinetic energy, and Ki is the initial kinetic energy.
We can rearrange this equation to solve for Kf:
Kf = Ki + W = Ki + Fd cos(theta)
a) Kf = 150 J + (10 N)(15 m)cos(90°) = 150 J
b) Kf = 300 J + (200 N)(1.5 m)cos(180°) = 0 J
c) Kf = 200 J + (25 N)(4 m)cos(0°) = 300 J
d) Kf = 450 J + (15 N)(30 m)cos(150°) = 112.5 J
Ranking from greatest to least final kinetic energy:
c) Ki=200J F=25N d=4m theta=0 degrees
a) Ki=150J F=10N d=15m theta=90 degrees
d) Ki=450J F=15N d=30m theta=150 degrees
b) Ki=300J F=200N d=1.5m theta=180 degrees
