A curve of radius 68m is banked for a design speed of 93 km/hr.
If the coefficient of static friction is 0.35 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.]
need both the max and min speeds
Ive tried yalls examples on similar problems and yet i remain off

-- From 1 to 3 seconds, the acceleration is 2.5 m/s².  (It changes suddenly at 3 seconds.)

-- At 2 seconds, the speed is 2.5 m/s .

-- At 2 seconds, the position is 1.25 meters.

BE CAREFUL !

I don't know where you got this graph, but you have to be very very careful when you try to read it.  The Y-axis is not at time=0.  It's at time=1.  And all the whole-number seconds are between the blue lines.

Answer:

Albert Einstein was from Germany he was born theoritical physicist, from childhood only he loved mechanical toys, he was highly gifted in Mathematics, He was a world citizen and a scientific genius too. His contribution were:

1) he developed the theory of relativity

2) he also discovered the process of nuclear fission

3)he developed the quantum theory of specific heat

4)theory of stimulated emission, on which laser device technology is based

5) law of photoelectric effect

hope it helped you :)

To produce a south pole at the right end of the coil in a solenoid diagram, the current must be flowing from left to right.

To provide an explanation, a solenoid is a coil of wire that produces a magnetic field when an electric current is passed through it.

The direction of the magnetic field depends on the direction of the current flow in the coil. In order to produce a south pole at the right end of the coil, the current must be flowing from left to right in the solenoid diagram.

In summary, to produce a south pole at the right end of the coil in a solenoid diagram, the current must be flowing from left to right.

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Answer:

1m

Explanation:

The conversion is 1mm = 0.001m. So all we need to do to find how many mm there are in a meter, all we need to do is divide by a 1000;

1000 / 1000 = 1m

Best of Luck!

AP Physics 1 is a college-level introductory physics course designed to give high school students an understanding of the fundamental principles of physics.

The course covers topics such as mechanics, waves, thermodynamics, electricity, and magnetism. Students in AP Physics 1 learn to think critically and solve problems using scientific inquiry, experimentation, and analysis. The course is structured to provide students with hands-on laboratory experience and to develop their skills in using math and quantitative analysis to explain physical phenomena. At the end of the course, students take an exam that can qualify them for college credit and demonstrate their mastery of the concepts and skills covered in the course.

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The acceleration of a particle is a= (-1.6 v1/2) m/s². The initial velocity of the particle is u = 8 m/s.

Now, let's use the formula: 2as = v² - u², where a = (-1.6v^(1/2)) m/s², u = 8 m/s, and v = 0 m/s 2 × (-1.6v^(1/2)) × s = 0 - 8²s = 64 / (2 × 1.6v^(1/2)) = 20v^(1/2)/4 = 5v^(1/2) meters.

This is the distance travelled by the particle before it stops.

We know that the final velocity of the particle is 0 m/s. The initial velocity of the particle is 8 m/s.

The acceleration of the particle is a = (-1.6v^(1/2)) m/s².

Let's use the formula to calculate the time it takes to stop the particle. It is:v = u + at 0 = 8 + (-1.6v^(1/2)) × t t = 8 / (1.6v^(1/2)) t = 5 / v^(1/2) seconds.

This is the time taken by the particle to come to rest.

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The particle travels approximately 12.5 meters before it comes to a stop. It takes approximately 5 seconds for the particle to reach zero velocity.

To determine the distance traveled before the particle comes to a stop, we need to integrate the velocity function over time. The given deceleration is expressed as a = -1.6√v , where v is the velocity in m/s. Since the initial velocity is 8 m/s, we can write the deceleration as a = -1.6√8. Integrating the acceleration with respect to velocity gives us the equation: ∫dv/(-1.6√v ) = ∫dt. Simplifying the integral and solving for t gives us t = 5 seconds.

To find the distance traveled, we integrate the velocity function with respect to time. The velocity function is given by dv/dt = -1.6√v. Separating variables and integrating, we get ∫dv/√v  = ∫-1.6dt. Evaluating the integral and substituting the limits (from v = 8 m/s to v = 0), we find √v = -1.6t + C. Applying the initial condition v(0) = 8, we can solve for C and obtain C = √8. Plugging in the values for t and C, we get √v = -1.6t + √8. Squaring both sides and solving for v, we find v = \((1.6t - \sqrt{8} )^{2}\). Integrating the velocity function again with respect to time, we get ∫\((1.6t - \sqrt{8} )^{2}\) dt = ∫ds. Evaluating the integral and substituting the limits, we find s = 12.5 meters.

Therefore, the particle travels approximately 12.5 meters before coming to a stop.

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Answer:

Thermal Energy. Thermal energy is the internal energy of an object due to the kinetic energy of its atoms and/or molecules. The atoms and/or molecules of a hotter object have greater kinetic energy than those of a colder one, in the form of vibrational, rotational, or, in the case of a gas, translational motion.

Explanation:

By shooting past it's equilibrium position and then oscillate before settling to the equilibrium position is characterize the response of the mass once you let go. So, option A is corect choice.

The given mass-spring-damper system can be represented by the differential equation:

\(my'' + \mu_fy' + k\timesy = F_{ext}\)

where y is the displacement of the mass from its equilibrium position, and \(F_{ext}\) is any external force acting on the system.

To determine the response of the mass once you let go, we need to solve the above differential equation for the initial condition y(0) = 0.2 and y'(0) = 0 (assuming that the mass is released from rest).

To solve the differential equation, we first need to determine the damping ratio, which is given by:

damping ratio (ζ) = \(\mu_f / (2 \times \sqrt{(k \times m)})\)

Substituting the given values, we get:

damping ratio (ζ) = \(7 / (2 \times \sqrt{160 \times 80})\) = 0.1106

Since the damping ratio is less than 1, the system is underdamped.

Therefore, the response of the mass once you let go will oscillate with a decreasing amplitude until it reaches its equilibrium position.

The frequency of oscillation (ω) can be determined using the following formula:

ω = \(\sqrt{(k / m - \zeta ^2 times (\mu_f^2 / 4 \times m^2))}\)

Substituting the given values, we get:

ω = \(\sqrt{160 / 80 - 0.1106^2 \times (7^2 / (4 \times 80^2)}\)= 4.352 rad/s

The time period of oscillation (T) can be determined using the formula:

T = 2π / ω

Substituting the value of ω, we get:

T = 2π / 4.352 = 1.444 s

Therefore, once you let go, the mass will oscillate around its equilibrium position with a decreasing amplitude and a time period of 1.444 s until it eventually comes to rest.

Hence, the correct answer is option A: "It would shoot past its equilibrium position and then oscillate before settling to the equilibrium position."

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Question:-

you have a mass spring damper system as descried by

\(m\frac{d^2y}{dt^2}+\mu_f\frac{dy}{dt}  +ky =F_{ext}\)

where

m= 80 kg

\(\mu_f\)  = 7 N*s/m

k = 160 N/m

The unit of Newtons (N) is equivalent to kg m/s²

If you were to displace the mass by 0.2 m from its equilibrium position, how would you characterize the response of the mass once you let go? (Hint: you need to determine the value of the damping ratio).

a. It would shoot past it's equilibrium position and then oscillate before settling to the equilibrium position

b. It will approach the equilibrium position very slowly but not oscillate.

c. The answer depends on the value of the time constant

d. The system will be critically damped.

Answer:

R2 = 300 Ohms

Explanation:

Let the two resistors be R1 and R2 respectively.

RT is the total equivalent resistance.

Given the following data;

R1 = 100 Ohms

RT = 75 Ohms

To find R2;

Mathematically, the total equivalent resistance of resistors connected in parallel is given by the formula;

\( RT = \frac {R1*R2}{R1 + R2} \)

Substituting into the formula, we have;

\( 75 = \frac {100*R2}{100 + R2} \)

Cross-multiplying, we have;

75 * (100 + R2) = 100R2

7500 + 75R2 = 100R2

7500 = 100R2 - 75R2

7500 = 25R2

R2 = 7500/25

R2 = 300 Ohms

In a photovoltaic system, an inverter is required to connect the DC current of the solar panel to the AC current of an electrical grid. The correct option is B.

The solar panels in a photovoltaic system generate DC (direct current) electricity. However, most electrical grids operate on AC (alternating current) electricity.

The role of the inverter is to convert the DC electricity produced by the solar panels into AC electricity that can be fed into the electrical grid or used to power electrical devices.

The inverter performs the important function of converting the type of current to match the requirements of the grid, enabling the efficient utilization of solar energy and facilitating the integration of solar power systems with the existing electrical infrastructure.

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Answer:

The temperature of an object increases when the molecules that make up that object move faster. Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

When a rise in temperature causes atoms and molecules to move faster Then thermal energy is produced as they collide with each other.

Thermal energy is produced in a substance when a rise in temperature causes atoms and molecules to move at a higher speed and result they collide with each other. The energy produced from the temperature of the heated material is known as thermal energy.

Thermal Energy or internal Kinetic Energy is due to the random motion of molecules in a system. The thermal energy of a given system is directly proportional to the temperature.

The greater the temperature of the system, the greater the movement of molecules within a given system, and the greater the thermal energy of the system.

The thermal energy is dependent on the temperature which is dependent on the motion of the molecules. As a result, the more molecules that are present within the system, the greater the amount of movement which raises the temperature and eventually thermal energy.

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Answer:

In the given function b(t), the variable t represents the number of years after 2008. The   domain of this function is . The range more than 258.7 would not make sense. The graph of the function is always continuous

The given function b(t) shows the population of bobcats in northern Arizona since 2008. Therefore the variable t represents the number of years after 2008.

Since t represents the number of years after 2008, which is either positive or zero, therefore the domain of this function is .

The given function is a quadratic function and the coefficient of  is negative, so it is a downward parabola. The range above the y-coordinate of the vertex doesn't make any sense.

The vertex of parabola is defined by .

Vertex of the given function is (4.2,258.7).

Thus, the range more than 258.7 would not make sense for this function.

Since the given function is a polynomial function and polynomial functions are always continuous, therefore the graph of the function is always continuous

HOPE THIS HELPS <3

when you get the answer please tell me

Answer:

2682

Explanation:

Work done is given by :

Work = Force x distance

         =  mg x d

So, work done in lifting the box of 23 kg up to my waist of 1 m high is :

W = mg x d

   = 23 x 9.18 x 1

   = 211.14

Now work done carrying the box horizontally 6 meters across the room is

W = mg x d

   = 23 x 9.18 x 6

   = 1266.84

Work done in placing the box on the shelf that is 5.7 m above the ground is

W = mg x d

   = 23 x 9.18 x 5.7

   = 1203.49

So the total work done is = 211.14 + 1266.84 + 1203.49

                                          = 2681.47

                                          = 2682 (rounding off)

Answer: Plato

Explanation: To find out whether a product is scientifically sound, check the FDA standards for the product. Another option is to ask a medical expert, such as a doctor or a nutrition scientist, whether the product is scientifically sound.

hope this helps

We can check the superfood or diet plan whether it is complying FDA standard or not. Another way is to send it to lab for testing which will gives information about the nutrient content used and its benefits as well as effects.

FDA is Food and Drug Administration that coordinates the evaluation, development, maintenance, and adoption of health and regulatory data standards to ensure that common data standards are used throughout the agency.

Superfood is a marketing term for food claimed to confer health benefits resulting from an exceptional nutrient density.

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Answer:

the answer is true Induction charging is a method used to charge an object without actually touching the object to any other charged object.

Explanation:

Answer:

A

Explanation:

inertia Equation for All Object is k m R²

inertia Equation of Hollow Cylinder I = m R²

inertia Equation of Solid Cylinder I = ½ m R²

inertia Equation of Hollow Sphere I = ⅔ m R²

inertia Equation of Solid Sphere I = 2/5 m R²

to find the speed needed we can use Mechanical Energy (ME). or Total Energy.

ME = Translation Kinetic Energy + Rotation Kinetic Energi

ME = ½ m v² + ½ I w²

ME = ½ m v² (1 + k)

v² = 2ME / m(1+k)

sinnce all objects have the same mass, we can figure that v² is proportionally with 1/(1+k)

v²(hc) = 1/(1+1) = ½ = 0.5

v = 0.707

v²(sc) = 1/(1+½) = 2/3 = 0.67

v = 0.818

v²(hs) = 1/(1+⅔) = 3/5 = 0.6

v = 0.744

v²(ss) = 1/(1+²/5) = 5/7 = 0.71

v = 0.842

these is the ratio of speed they produce in the end of the arc with initial speed = 0 m/s

so, if we must give speed to the object so that it can reach the end of the arc, the fastest speed is given to hollow cylinder and the slowest speed is given to Solid Sphere

Then the answer is

HC, HS, SC, SS

Solid sphere, solid cylinder, hollow sphere, hollow cylinder  correctly lists the objects in order from fastest to slowest speed needed to make it through the arc.

A body's inertia is a characteristic that makes it resist attempts to move it or, if it is already moving, to change the speed or direction of it.

Mathematically:

inertia All Object is = k m R²

inertia of Hollow Cylinder I₁ = m R²

inertia of Solid Cylinder I₂ = ½ m R²

inertia of Hollow Sphere I₃ = ⅔ m R²

inertia of Solid Sphere I₄ = 2/5 m R²

Total kinetic energy of a body while it roll without slipping  = Translation Kinetic Energy + Rotation Kinetic Energi

= ½ m v² + ½ I w²

= ½ m v² (1 + k)

= 2 KE / m(1+k)

Since all objects have the same mass and, v² can be expressed as proportionally with 1/(1+k).

For hollow cylinder: v₁² = 1/(1+1) = ½ = 0.5

v₁ = 0.707

For solid cylinder: v₂²= 1/(1+½) = 2/3 = 0.67

v₂ = 0.818

For hollow sphere: v₃² = 1/(1+⅔) = 3/5 = 0.6

v₃ = 0.744

For solid sphere: v₄² = 1/(1+²/5) = 5/7 = 0.71

v ₄= 0.842

The objects in order from fastest to slowest speed needed to make it through the arc are correctly listed as:

solid sphere > solid cylinder > hollow sphere >  hollow cylinder.

Option (C) is correct.

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Answer: The answer is D. Thermal Energy.

Explanation:

Thermal energy is a type of kinetic energy owing to the fact that it results from the movement of particles.

Viscosity, the resistance to flow, is determined by the strength of the intermolecular attractions. Substances with strong intermolecular forces are more viscous than are substances with weak intermolecular forces. Temperature also affects the viscosity of a given liquid. As temperature increases, the corresponding increase in kinetic energy overcomes some of the intermolecular attractions. This decreases the overall viscosity of the liquid and allows the liquid to flow more freely.

Surface tension is the tendency of liquids to minimize their surface area. Molecules at the surface of the liquid have no liquid molecules above them with which to interact, so they experience a downward pull. This downward pull causes all liquids to minimize their surface area. Cohesion is the attraction of atoms and molecules to like particles. Adhesion, the attraction to different particles, is also possible, provided the other particle can form intermolecular forces. Cohesion and adhesion help to explain capillarity, the ability of a liquid to flow against gravity up a narrow tube.

Viscosity refers to a fluid’s resistance to flow. A high-viscosity fluid will be thicker and flow less freely than a low-viscosity fluid. Intermolecular forces in a liquid can also impact its viscosity. Stronger intermolecular forces result in a higher viscosity. Temperature affects viscosity because it influences kinetic energy, which can overcome some of the intermolecular attractions in a liquid, leading to a lower viscosity.

Surface tension is the tendency of a liquid to minimize its surface area. The molecules at the surface of a liquid experience a downward pull since they have no other liquid molecules above them with which to interact. The cohesive forces between liquid molecules give rise to surface tension. Cohesion is the attraction of atoms and molecules to like particles, while adhesion is the attraction to different particles. Capillarity is the ability of a liquid to flow against gravity up a narrow tube, and it occurs due to both cohesion and adhesion.

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The activity of the sample after 5 hours is 2.5 * 10^9 dps or 2.5 * 10^9 Bq

The activity of a radioactive sample refers to the rate at which its nuclei decay, and it is typically measured in units of disintegrations per second (dps) or becquerels (Bq).

To determine the activity of the sample after 5 hours, we need to consider the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the nuclei in a sample to decay.

Given that the half-life of the nuclei in the sample is 2.5 hours, we can calculate the number of half-lives that occur within the 5-hour period.

Number of half-lives = (Time elapsed) / (Half-life)

Number of half-lives = 5 hours / 2.5 hours = 2

This means that within the 5-hour period, two half-lives have occurred.

Since each half-life reduces the number of nuclei by half, after one half-life, the number of nuclei remaining is (1/2) * (10^10) = 5 * 10^9 nuclei.

After two half-lives, the number of nuclei remaining is (1/2) * (5 * 10^9) = 2.5 * 10^9 nuclei.

The activity of the sample is directly proportional to the number of remaining nuclei.

Therefore, After 5 hours, the sample has an activity of 2.5 * 109 dps or 2.5 * 109 Bq.

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The angle θ is approximately 0.688°, and the angle θ' is approximately 1.988°.

To determine the angles θ and θ' in the given scenario, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the media involved. Snell's Law can be stated as follows:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:

n₁ is the refractive index of the medium of incidence (in this case, air with a refractive index close to 1),

θ₁ is the angle of incidence,

n₂ is the refractive index of the medium of refraction (in this case, linseed oil with a refractive index of 1.48), and

θ₂ is the angle of refraction.

Let's solve for the unknown angles θ and θ' using the given information.

Given:

Angle of incidence θ = 1°

Refractive index of linseed oil n₂ = 1.48

We need to find the angle of refraction θ₂.

Using Snell's Law, we have:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Since the refractive index of air (n₁) is approximately 1, we can simplify the equation to:

sin(θ₁) = n₂ * sin(θ₂)

Plugging in the values:

sin(1°) = 1.48 * sin(θ₂)

We can now solve for θ₂:

θ₂ = arcsin(sin(1°) / 1.48)

Calculating this value, we find:

θ₂ ≈ 0.688°

Now, let's determine the angle θ'.

Given:

Angle of refraction θ₂ = 0.688°

Refractive index of linseed oil n₂ = 1.48

We need to find the angle of incidence θ'.

Using Snell's Law, we have:

n₂ * sin(θ₂) = n₁ * sin(θ')

Since the refractive index of air (n₁) is approximately 1, we can simplify the equation to:

n₂ * sin(θ₂) = sin(θ')

Plugging in the values:

1.48 * sin(0.688°) = sin(θ')

Solving for θ', we find:

θ' = arcsin(1.48 * sin(0.688°))

Calculating this value, we get:

θ' ≈ 1.988°

Therefore, the angle θ is approximately 0.688°, and the angle θ' is approximately 1.988°.

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When the pedaling cyclist uses a generator (dynamo) to light his bicycle lamp, the energy change is from mechanical to electrical.

The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.

Thus, we can conclude the following as it relates to energy changes;

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Answer:

Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².

Explanation:

To find the magnitude of acceleration at the instant when velocity is zero, we need to differentiate the given velocity equation with respect to time (t) to obtain the acceleration equation.

Given:

Velocity equation: v(t) = 22 - 3.8t^2

Differentiating the velocity equation with respect to time, we get:

a(t) = d(v(t))/dt = -2 * 3.8t

To find the magnitude of acceleration at the instant when velocity is zero, we need to solve for t when v(t) = 0.

0 = 22 - 3.8t^2

3.8t^2 = 22

t^2 = 22/3.8

t^2 ≈ 5.789

Taking the square root of both sides, we find:

t ≈ √(5.789)

t ≈ 2.403

Now we can substitute this value of t into the acceleration equation to find the magnitude of acceleration at that instant:

a(t) = -2 * 3.8 * 2.403

a(t) ≈ -18.258

Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².

A goldfish swims in a bowl of water at 20°C over a period of time, fish transfer 120j to the water as a result of its metabolism, the change in entropy of the water is 0.409 J/K.

In other words, the increase in disorganization within a system is what is referred to as entropy, which is defined as the measurement of degree of randomness. Entropy is a unitary measure of the amount of thermal energy in a system that cannot be used to carry out useful work. The quantity of entropy is also a gauge of a system's molecular disorder, or randomness, as work is produced by ordered molecular motion.

change in entropy = dQ / T

change in entropy = 120 / (273 + 20 ) = 0.409 J/K.

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If the student replaced the water in the calorimetry device with an ice bath at 0°C, the experimental results would differ in several ways:

Temperature Change: Instead of measuring the change in temperature of the water, the student would measure the change in temperature of the ice bath. As heat is transferred from the surroundings to the ice bath, the ice will melt and the temperature of the ice bath will increase until it reaches 0°C. The temperature change observed in the experiment would be different from that of the water bath.
Heat Capacity: The heat capacity of the ice bath would be different from that of the water bath. Ice has a lower heat capacity than water, meaning it requires less heat energy to raise its temperature. This would affect the amount of heat absorbed or released during the reaction and lead to different experimental results.
Enthalpy Change: The enthalpy change calculated from the experiment would be specific to the reaction being studied. However, the enthalpy change determined using an ice bath would be based on the heat exchange with the ice bath, rather than the water bath. The enthalpy change values would differ due to the different heat capacities and temperature changes involved.
Overall, using an ice bath instead of a water bath would result in different temperature changes, heat capacities, and enthalpy change values in the experimental results.

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On a wet road, you would need to adjust your speed to 5-10 mph slower than normal.So option a is correct.

On a wet road, you should adjust your speed to ensure that you can drive safely. This is because water causes tyres to lose traction with the road. If you increase your speed on a wet road, you'll have less control over your vehicle. When the road is wet, your vehicle's tyres may not be able to grip the road as well as they would on a dry road.When driving on wet roads, you should maintain a safe distance between your vehicle and the car in front of you. This provides you with enough space to stop safely if the car in front of you stops suddenly.In addition, when driving on wet roads, it's best to avoid sudden steering or braking movements. This will cause your car to skid. Therefore, you should slow down and move more gently on a wet road, and always adjust your speed to 5-10 mph slower than normal.Therefore option a is correct.

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Answer:

Option B

Explanation:

since,

4800km=0.48cm

Therefore,

1cm=4800/0.48

1cm=10,000km

The equation for energy given by the friend, energy = distance × force, is incorrect.

The equation presented by the friend, energy = distance × force, is not consistent with the principles of dimensional analysis. Dimensional analysis involves examining the units of the quantities involved in an equation to ensure they are consistent on both sides of the equation. In this case, the units on the right side of the equation do not match the units of energy.

In the equation, distance is given as a unit of length, typically measured in meters (m). Force is given as a unit of mass multiplied by acceleration, typically measured in kilograms (kg) times meters per second squared (m/s²). Multiplying distance by force would yield units of meters multiplied by kilograms multiplied by meters per second squared, which is not equivalent to the units of energy.

The correct equation for energy should involve the dot product or scalar product of the distance and force vectors. The dot product takes into account both the magnitude of the force and the displacement vector of the distance. It would result in a scalar quantity, which is the correct representation of energy. Therefore, the friend's equation lacks the dot product operator, and that's why we know it is incorrect without even looking at the specifics of the problem.

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