the w8 x 67 wide-flange a-36 steel column can be assumed fixed at its base and pinned at its top. determine the largest axial force p that can be applied without causing it to buckle.
Answers
The largest axial force that can be applied to the w8 x 67 wide-flange A-36 steel column without causing it to buckle is 179 kips.
To determine the largest axial force that can be applied to the w8 x 67 wide-flange A-36 steel column without causing it to buckle, we need to use Euler's formula. Euler's formula relates the critical buckling load (Pcr) to the column's effective length (L) and its moment of inertia (I). The formula is Pcr = (pi^2 * E * I) / L^2, where E is the modulus of elasticity.
First, we need to find the effective length of the column. Since the column is fixed at its base and pinned at its top, its effective length is equal to its actual length. Let's assume that the actual length of the column is 10 feet or 120 inches.
Next, we need to find the moment of inertia (I) of the column. For a W8 x 67 section, the moment of inertia about the strong axis (x-x axis) is 23.5 in^4.
Finally, we need to find the modulus of elasticity (E) of A-36 steel, which is approximately 29,000 ksi.
Plugging in the values in Euler's formula, we get:
Pcr = (pi^2 * 29,000 ksi * 23.5 in^4) / (120 in)^2 = 179 kips
Therefore, the largest axial force that can be applied to the w8 x 67 wide-flange A-36 steel column without causing it to buckle is 179 kips.
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Related Questions
Rewrite the following sentence in the negative form >Each library contains 3000 brand new books
Answers
A hiker walks with an average speed of 2.6 M Square what distance in kilometers does the hiker travel in a time of 2.8 hours
Answers
Answer:
The answer is "26.208 km"
Explanation:
Given value:
\(\to S= 2.6 \ \frac{m}{s}\\\\\to t= 2.8 \ hours\)
Formula:
\(d= st\\\\d= 2.6 \times 2.8 \times \frac{60 \times 60}{1000}\\\\d= 26.208\ km\)
A plane mirror is useful for seeing:
Answers
They are used to see round dangerous bends
PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST The actual subject is Science but they dont have that as a option in pick a subject
Answers
18. A submerged stone weighs 254 newtons, but out of the water it weighs 1235 newtons. The density of the water is1000 kilograms per cubic meter. The volume of the stone is most nearly(a) 0.100 m^3(b) 0.206 m^3(c) 0.254 m^3(d) 1.24 m^3
Answers
ANSWER:
(a) 0.100 m^3
STEP-BY-STEP EXPLANATION:
We have that the force is equal to mass times gravity, therefore, we can calculate the mass, because the difference in force would be the volume of the stone.
Therefore
\(\begin{gathered} F=m\cdot a \\ m=\frac{F}{a} \\ m=\frac{1235-254}{9.8}=100.1\text{ kg} \end{gathered}\)Now, we know that the density is equal to the quotient between the mass and the volume, therefore we can calculate the volume like this:
\(\begin{gathered} d=\frac{m}{v} \\ v=\frac{m}{d} \\ v=\frac{100.1}{1000} \\ v=0.1001\cong0.100m^3 \end{gathered}\)Therefore the volume of the piece is 0.100 cubic meters.
Which statements about observations and inferences are correct? Select all that apply.
Answers
The following are the accurate observations and inferences:
The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. Using scientific tools to perceive and record data is another way that observation may be used in science. The phrase may also be used to describe any data gathered for the scientific endeavor. Observations can be quantitative if a numerical value is assigned to the seen phenomena by counting or measuring, or qualitative if just the existence or absence of a quality is documented.Inferences are processes in reasoning that connect premises to logical conclusions; the word "infer" derives from the Latin 'inferrere', which meaning to "carry on." The two types of inference are generally separated into deduction and induction in theory. Deduction is inference that draws logical conclusions from premises that are known to be true or that are presumed to be true, whereas valid inference laws are examined in logic. Induction is drawing a general conclusion from specific facts.To learn more about the observations, visit :
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During an autumn storm, a 0.012-kg hail stone traveling at 20.0 m/s made a0.20-cm-deep dent in the hood of Darnell's new car. What average force didthe car exert to stop the damaging hail stone?
Answers
Answer:
1200 N
Explanation:
First, we need to calculate how much time the force was applied. If the stone traveled at 20.0m/s and made a 0.20 cm deep dent, the time is equal to
\(\text{ Avg }speed=\frac{distance}{time}\Rightarrow time=\frac{distace}{Avg\text{ }speed}\)Where the distance is 0.20 cm = 0.0020 m and the average speed can be calculated as:
\(\text{ avg speed = }\frac{v_i+v_f}{2}=\frac{20\text{ m/s + 0 m/s}}{2}=10\text{ m/s}\)Therefore, the time is equal to
\(time=\frac{0.0020\text{ m}}{10\text{ m/s}}=0.0002\text{ s}\)Then, the force can be calculated using the following equation for impulse
\(\begin{gathered} Ft=mv \\ F=\frac{mv}{t} \end{gathered}\)Where m is the mass, v is the speed and t is the time, so replacing m = 0.012 kg, v = 20 m/s and t = 0.0001 s, we get
\(F=\frac{0.012\text{ kg \lparen20 m/s\rparen}}{0.0002\text{ s}}=1200N\)So, the average force was 1200 N
During autumn, the storm travels at a speed of 20 m/s, then the average force the car has to exert to stop the damaging hail storm is 1200 N.
What is Force?A force in physics is an effect that has the ability to modify an object's motion. A bulk object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can be used to describe force. Being a vector quantity, a force also has magnitude and direction. The SI unit of newton is used to measure it (N). The letter F symbolizes for force.
As per Newton's second law's original formulation, an object's net force is equal to the speed at which momentum is changing over time.
According to the given information in the question,
Speed, s= 20 m/s
Average speed, s = Distance/Time
s = [v(i) + v(f)] / 2
s = (20 + 0)/2
s = 10 m/s
Now calculate the time,
Time, t = 0.0020/10
t = 0.0002 seconds.
Use the equation for impulse,
f × t = mv
⇒f = mv/t
f= (0.012 × 20)/0.0002
f = 1200 N
Therefore, the force applied is 1200 N.
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1) anything that has mass and takes up space is called
A. Tissues
B. Mass
C. Matter
D. Atomic number
E. Weight
2) mechanical energy is
A. Found in machinery only
B. Usually measured at the atomic level
C. The sum of the chemical and thermal energy of an object
D. The sum of the kinetic and potential energy of an object
( please answer it guys i really bad at my physics TnT))
Answers
2) The sum of the kitenic and potential energy of an object
Not sure about the second one but hope this helps
\(\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ \)
Anything that has mass and takes up space is :-\(\pink{\boxed{\sf{↪Option.c↩}}}\)
→Matter✓
mechanical energy is\(\pink{\boxed{\sf{↪Option.d↩}}}\)
→The sum of the kinetic and potential energy of an object✓
___________________☃️\(\sf{\:мѕнαcкεя\: ♪...}\)
A 17.5-cm-diameter loop of wire is initially oriented perpendicular to a 1.3-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.15 s .
Answers
The magnitude of the average induced emf in the loop during the rotation is 3.7 V.
When a loop of wire is rotated in a magnetic field, an induced electromotive force (emf) is generated in the loop. The magnitude of this induced emf can be calculated using Faraday's law of electromagnetic induction:
ε = -N * (ΔΦ/Δt)
where ε is the induced emf, N is the number of turns in the loop, ΔΦ is the change in magnetic flux through the loop, and Δt is the time interval during which the change occurs.
In this case, the loop has a diameter of 17.5 cm, which corresponds to a radius of 8.75 cm (or 0.0875 m). The area of the loop is given by A = π * r^2, where r is the radius.
Therefore, the initial magnetic flux through the loop is Φ = B * A, where B is the magnetic field strength. Given that the magnetic field is 1.3 T, we can calculate the initial magnetic flux.
Φ = 1.3 T * π * \((0.0875 m)^2\)
Next, we need to calculate the change in magnetic flux as the loop rotates. Since the loop is initially oriented perpendicular to the magnetic field, and then it is rotated to become parallel, the change in magnetic flux is simply the difference between the final and initial magnetic fluxes.
ΔΦ = Φ_final - Φ_initial
Since the final magnetic flux is zero (as the loop becomes parallel to the field direction), the change in magnetic flux is -Φ_initial.
Finally, we can substitute the values into the formula for the induced emf to find its magnitude:
ε = -N * (-Φ_initial / Δt)
In this problem, the time interval Δt is given as 0.15 s.
ε = N * (Φ_initial / Δt)
Calculating the values, we obtain:
ε = N * (1.3 T * π * (0.0875 m)^2) / 0.15 s
Simplifying this expression will give us the magnitude of the average induced emf in the loop during the rotation.
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a ball rolls from rest down an incline with a uniform acceleration of 4m/s². what is it speed after 8 seconds
Answers
Below please discuss:
1. What is it about lithium that is so essential to devices such as iPhones and electric cars?
2. What is it about lithium mining methods that make it a particular environmental hazard?
3. If we have a benefit from greater uses of batteries--for example, more electric vehicles reducing CO2 emissions--what for you is the tipping point where the benefit of lithium outweighs its environmental costs?
Physical geology subject
Answers
Lithium is essential to devices such as iPhones and electric cars because of its unique properties that make it an ideal material for rechargeable batteries. Lithium-ion batteries, which are widely used in these devices, offer high energy density, lightweight design, and longer lifespan compared to other types of batteries.
The abundance of lithium ions allows for efficient energy storage and discharge, making it crucial for powering portable electronics and electric vehicles.
Lithium mining methods pose specific environmental hazards due to their extraction processes and the potential impact on local ecosystems. One common method of lithium extraction is through open-pit mining, which involves removing large amounts of topsoil and vegetation. This can lead to habitat destruction, soil erosion, and loss of biodiversity in the surrounding areas. Additionally, lithium mining requires significant water resources, potentially leading to water scarcity and pollution as chemicals are used in the extraction and purification processes. Improper disposal of mining waste can also result in soil and water contamination, affecting local ecosystems and potentially human health.
The tipping point where the benefit of lithium outweighs its environmental costs in the context of greater battery usage, such as in electric vehicles, is a complex and subjective consideration. It depends on various factors, including the scale of lithium extraction, the efficiency of recycling processes, the development of alternative battery technologies, and the overall environmental impact of the energy sources used for charging those batteries. To determine the tipping point, a comprehensive analysis is needed to evaluate the net environmental impact, considering the entire life cycle of lithium batteries from mining to disposal. This analysis should assess factors such as greenhouse gas emissions, land use, water consumption, waste management, and the potential for mitigating environmental impacts through sustainable mining practices, recycling initiatives, and renewable energy integration. Striking a balance between reaping the benefits of lithium in reducing CO2 emissions and minimizing its environmental costs requires careful consideration and the implementation of sustainable practices throughout the entire battery supply chain.
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What happens to the density of a fluid as it temperature increases/decreases?
Answers
an increase in sound level from 30 db to 50 db requires an increase in sound intensity by a factor of:
Answers
Loudness increases by 10 dB for every dB increase in sound intensity. A 40-decibel light rainstorm is 100 times louder than a whisper, whereas a 30-decibel "silent" room is 10 times louder than a 20-decibel whisper. Loud noises can be harmful.
50 dB is how much louder than 20 dB?A 10 dB rise results in a two-fold increase in volume. The loudness will therefore rise by nearly 8 times with a 30 dB increase (from 20 dB to 50 dB).
Decibels are measured on a logarithmic scale using a power of ten, which might be perplexing. For those of you without advanced math degrees, this simply implies that the sound intensity doubles for every 10 decibel rise.
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If a car accelerates from rest at a constant 4 m/s
, how long will it take for the car to reach a
velocity of 28 m/s?
Answers
Answer:
Time, t = 7 seconds.
Explanation:
Given the following data;
Initial velocity = 0m/s (since it is starting from rest).
Acceleration, a = 4 m/s²
Final velocity, v = 28 m/s
To find the time, we would use the first equation of motion given by the formula;
V = u + at
Substituting into the formula, we have;
28 = 0 + 4*t
28 = 4t
Time, t = 28/4
Time, t = 7 seconds.
A main sequence star does not expand or contract due to the balance between the internal heat pushing outward and the weight of the material pressing inward due to gravity. this state of maintaining a constant size is known as:
Answers
The state of maintaining a constant size by the sequence star due to balance between the internal heat pushing outward and the weight of the material pressing inward due to gravity is hydrostatic equilibrium.
A main sequence star is a stable one. There is no overall change. This is so that the fluid's pressure gradient acting outward balances the material's gravity acting inward. The star is made of gases. It is a fluid system. Hydro-static equilibrium is the name given to this type of equilibrium.The star may have fallen into a black hole under the influence of gravity, although this is not exactly what is occurring.
The star generates its energy through fusion, which turns hydrogen into helium. Much more heat is generated in this reaction.
Due to increased internal pressure, the star is now moving outward.
The forces of gravity acting internally and outside balance one another.
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Compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2. 00 m. Assume the electrons have a mass of 9. 11 × 10–31 kg and a charge of 1. 61 × 10–19 C. Round to two decimal places. Fe = × 10–29 N Fg = × 10–71 N F Subscript e baseline over F Subscript g baseline. = × 1042.
Answers
Fₑ/Fg is 9.63 × 10⁻²². To compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2.00 m we can use the Coulomb's law and Newton's law of gravitation formula. The formula for the electric force between two charges is given as: F = kq₁q₂ / r²
Where, k = Coulomb constant = 9 × 10⁹ Nm²C⁻², q₁ and q₂ = charges on the two particles, r = distance between the two particles
For two electrons, q₁ = q₂ = -1.61 × 10⁻¹⁹ , CR = 2.00 m
F = 9 × 10⁹ × (-1.61 × 10⁻¹⁹)² / (2.00)²
= 2.31 × 10⁻²⁸ N
The formula for gravitational force between two particles is given as: F = Gm₁m₂ / r²: where, G = gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², m₁ and m₂ = masses of the two particles, r = distance between the two particles
For two electrons, m₁ = m₂ = 9.11 × 10⁻³¹ kg, R = 2.00 m
Substituting the values in the formula we get, F = 6.67 × 10⁻¹¹ × (9.11 × 10⁻³¹)² / (2.00)²
= 2.40 × 10⁻⁷ N
Thus, the magnitude of the electromagnetic force is 2.31 × 10⁻²⁸ N and the magnitude of the gravitational force is 2.40 × 10⁻⁷ N.
The ratio of Fe/Fg= (2.31 × 10⁻²⁸)/(2.40 × 10⁻⁷)
= 9.63 × 10⁻²²
Thus, Fₑ/Fg is 9.63 × 10⁻²².
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Answer:
see picture
Explanation:
which of these methods is used to determine which component in a circuit isn't working properly? voltage test, ohm amp draw or hopscotching
Answers
All of these methods can be useful in identifying a faulty component in a circuit, and which one to use depends on the specific situation and the experience of the troubleshooter.
When a circuit component fails, it can cause the entire circuit to malfunction. Troubleshooting a circuit requires identifying the problematic component so that it can be replaced or repaired. There are different methods to determine which component is not working properly, including voltage testing, ohm amp draw, and hopscotching.
Voltage testing involves measuring the voltage at various points in the circuit to identify where the voltage drop occurs, which can indicate a faulty component.
Ohm amp draw involves measuring the resistance and current flow through each component to determine if any are outside of their expected range.
Hopscotching involves checking each component in the circuit one by one, starting from the power source, to see which one is causing the problem.
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a simple pendulum having a length of 2.99 m and a mass of 9.46 kg undergoes simple harmonic motion when given an initial speed of 2.18 m/s at its equilibrium position. determine its period. the acceleration due to gravity is 9.8 m/s 2 . answer in units of s.
Answers
The body goes through equilibrium position its displacement x is zero. Hence, acceleration also 0.
What is acceleration?
Acceleration rate at which velocity change with time, in terms of both speed and direction.
Sol-The restoring force in case of simple harmonic motion is an elastic force of the spring. It could be found by the use of Hooke's law F = - kx. Here k - the spring constant and x - deformation of the spring (change of its length from equilibrium position).
We see that this is a variables force that is depends on the given displacement of their mass-spring system of x. Minus sign tells us that the direction of this force is opposite to that of the displacement; as a result of this force brings the mass of the back to the equilibrium position (this is why we called it a restoring force).
As any force, restoring force could be found using Newtons second law F = ma, where m - mass of the body and a - acceleration of the body.
Now we can write:
When the body goes through equilibrium position its displacement x is zero. Hence, acceleration also 0.
BTW, the maximum value of the acceleration we will have when the amplitude of this mass-spring system is the maximum. At this points the direction of the mass-spring pendulum switches to the opposite. Those points we are call inflection points.
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what is kinetic energy, in your own words but be more detailed about what you say.
Answers
Kinetic energy is the energy when a object is in motion. ... energy gets transferred to the object, The energy transferred is kinetic energy, and it depends on the mass and speed.
Explanation:
Start with the atom diameter being as large as possible and interaction strength being as weakas possible.
What size are the force arrows in the middle of the atoms?
Answers
Start with the atom diameter being as large as possible and interaction strength being as weakas possible.
What size are the force arrows in the middle of the atoms is small.
The atomic diameter is the distance across the nucleus, measured in picometers (pm). The nucleus is at the core of the atom. It consists of protons and neutrons. The electrons circle the nucleus in shells or energy levels, which are shown as circles around the nucleus in atomic models.Atomic radius is a term that is often used synonymously with atomic diameter. The atomic radius is the distance from the center of the nucleus to the outermost shell of electrons, which determines the size of an atom.
The interaction strength refers to how strong the bonds are between atoms. The stronger the interaction, the closer the atoms are, and the harder it is to pull them apart. In comparison, if the interaction is weaker, the atoms are farther apart, and they can be pulled apart more easily. Consequently, if the atom diameter is large and the interaction strength is weak, the size of the force arrows in the middle of the atoms is small.
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Colombia does not have money to fund national sports leagues, let alone professional cyclists.
Answer True or False
True
False
Answers
explanation
Calculate the potential at the centre of a square of side √4.5 m which carries at its
four corners and charges of + 5 x 10° C, 2 x 10°C, -5 x 10° C and - 7 x 10°C
respectively
Answers
Thus, the total potential is then V_total = \(-1.2 * 10^9V\)
How to solve
The potential at a point due to a charge is given by V = kQ/r, where k is Coulomb's constant (~\(9x10^9 Nm^2/C^2\)), Q is the charge, and r is the distance from the charge.
The total potential at the center of the square is the sum of the potentials due to each charge.
The distance of each charge to the center is half the diagonal of the square, which is \(\sqrt2 * side/2 = \sqrt2 * \sqrt4.5/2 = 1.5m.\)
The total potential is then V_total
= \(k * [(510^8/1.5) + (210^8/1.5) - (510^8/1.5) - (710^8/1.5)] = -2 * k * 10^8 / 1.5 \\= -1.2 x 10^9 V.\)
Thus, the total potential is then V_total = \(-1.2 * 10^9V\)
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A vehicle moving with a uniform acceleration of 4 m/s² has a velocity of 8 m/s at
certain time What will its velocity be 2 s later
Answers
Initial velocity(u) = 4 m/s
time interval (t) = 2 second
We know that ,
v = u + at
v = 4 + 2×2 = 8 m/s
Therefore the velocity of vehicle after(when it's velocity was 4 m/s) 2 sec = 8 m/s
A ball of 0.5kg slows down from 5m/s to 3m/s. Calculate the work done in the process
Answers
Explanation:
m = 0.5kg
V = 3m/s - 5m/s = -2m/s
P = W/t = Fv
F = ma
W = Fvt
W = (0.5)(9.8)t = 4.9t
How is the amount of light entering our eyes controlled? What changes are made in the eye to enable it to flow on the object situated at different distance
Answers
Answer:
The amount of light that enters our eyes is controlled by two things: the size of the pupil and the iris. The pupil is the black hole in the center of your eye, and the iris is the colored part around the pupil. The iris can change the size of the pupil to control how much light gets in.
When it's dark, the iris makes the pupil bigger to let in more light so we can see better. And when it's bright, the iris makes the pupil smaller to block out some of the light so it doesn't hurt our eyes.
To see objects at different distances, the eye needs to adjust the shape of the lens. When we look at things that are far away, the lens becomes thinner and flatter. When we look at things that are close up, the lens becomes thicker and more curved. This allows the eye to focus the light on the right spot on the retina at the back of the eye.
The amount of light that enters our eyes is controlled by the size of the pupil and iris, and the shape of the lens changes to allow us to see objects at different distances.
I hope this helps! And if you could label my answer brainliest that would be awesome.
- Dante
what is the approximate distance from earth to the sun?
Answers
The approximate distance from the Earth to the Sun is about 93 million miles
What is the approximate distance from the Earth to the Sun?The average distance from the Earth to the Sun is about 93 million miles (149.6 million kilometers). This distance is known as an astronomical unit (AU) and it is used to measure distances within the solar system. It is important to note that this distance is not a constant and varies slightly over time due to the elliptical shape of Earth's orbit around the Sun.
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Consider the straight bar of a uniform elliptical cross-section. The semimajor and semiminor axes are a and b, respectively. Show that the stress function of the form + provides the solution for torsion of the bar. Find the expression of C and show that лазь3 a2 +b2 —2Ty Izx Тzy 2Tx лаbЗ» лазь and the warping displacement т(? — а?). -ху лазь3G
Answers
The stress function of the form Φ = C(x²- y²) provides the solution for torsion of the bar.
How can we determine the expression of C and derive the given equation?To determine the expression of C and derive the given equation, we consider the torsion of a straight bar with a uniform elliptical cross-section. The stress function Φ is assumed to have the form Φ = C(x²- y²), where C is a constant.
By substituting the stress function into the torsion equation and solving for the shear stress τxy, we find that τxy = 2GC(xsin(θ) - ycos(θ)), where G is the shear modulus and θ is the angular coordinate.
To find the expression of C, we compare this equation with the given equation and equate the terms. This leads us to C = Ty/(2G), where Ty is the applied torque.
By further substituting the expressions for x and y in terms of the semimajor and semiminor axes, we can rewrite the equation as τxy = Ty(a²+ b²- 2Jx/R²), where J is the torsional constant and R is the radius of the cross-section.
The warping displacement θ(Φ - Φ0) can be obtained by integrating the torsion equation, which involves the shear stress τxy and the differential area of the cross-section. This displacement can be expressed as θ(Φ - Φ0) = -G∫(τxy dA).
In summary, the stress function Φ = C(x²- y²) provides the solution for torsion of the bar, where C = Ty/(2G) and the derived equation is τxy = Ty(a²+ b² - 2Jx/R²). The warping displacement can be calculated through the integration of the torsion equation.
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do Seasonal changes impact the environment. A. True B. False
Answers
Answer:
A - True
Explanation:
Seasonal changes in precipitation and temperature affect soil moisture, evaporation rates, river flows, lake levels, and snow cover. Leaves fall and plants wither as cold and dry seasons approach. These changes in vegetation affect the type and amount of food available for humans and other organisms.
Answer:
Its true big dog
Explanation:
which is the correct statement regarding the work and impulse required to move a box on the floor i) from 2v to 3v; and ii) from 3v to 4v? a box is shown on a horizontal surface. which is the correct statement regarding the work and impulse required to move a box on the floor i) from 2v to 3v; and ii) from 3v to 4v? a box is shown on a horizontal surface. case i requires more work, but i and ii require the same amount of impulse; case i requires less impulse, but i and ii require the same amount of work; case i requires less work, but i and ii require the same amount of impulse; case i requires more impulse, but i and ii require the same amount of work; the two cases require the same amount of work and impulse;
Answers
The correct statement regarding the work and impulse required to move a box on the floor from 2v to 3v and from 3v to 4v is Case i requires less work, but i and ii require the same amount of impulse.
W = ΔKE
W = Work done
ΔKE = Change in Kinetic energy
ΔKE = 1 / 2 m ( v2 - v1 )²
J = m Δv
J = Impulse
m = Mass
Δv = Change in velocity
For ( i ),
W = 1 / 2 m ( ( 3 v )² - ( 2 v )² )
W = 1 / 2 m ( 9 v² - 4 v² )
W = 2.5 m v²
J = m ( 3 v - 2 v )
J = m v
For ( ii ),
W = 1 / 2 m ( ( 4 v )² - ( 3 v )² )
W = 1 / 2 m ( 16 v² - 9 v² )
W = 3.5 m v²
J = m ( 4 v - 3 v )
J = m v
Therefore,
i ) W1 < W2
ii ) J1 = J2
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Prediction 1-2: Suppose that the force is not exerted along the line of motion but is in some other direction. If you try to pull the IOLab up along the same ramp in the same way as before (again with a constant velocity), only this time with a force that is not parallel to the surface of the ramp, will the force sensor measure the same force, a larger force, or a smaller force? Note that, the force sensor measures the force only in the y-direction.
Answers
If the force is not exerted along the line of motion but is in some other direction, the force sensor will not measure the same force.
In fact, the force sensor will measure a larger force since the force is no longer parallel to the surface of the ramp.
The force sensor only measures the force in the y-direction, so if the force is not parallel to the surface of the ramp, there will be a component of the force that is perpendicular to the ramp.
This perpendicular component of the force will add to the force measured by the force sensor, resulting in a larger force reading.
However, since the IO Lab is still moving at a constant velocity, the force must be balanced by an equal and opposite force, which means that there must be a component of the force that is parallel to the surface of the ramp.
Therefore, the force exerted on the IO Lab will have both a perpendicular and parallel component, and the force sensor will measure the force in the y-direction, which will be a larger force than before.
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