A boulder rolls off a 100 meter cliff with a horizontal velocity of 2 m/s.
Make a sketch of the cliff and the boulder. Be sure to label the height of the cliff, the horizontal velocty of the
boulder, and the trajectory of the boulder

(a) The speed of the ball at the lowest point is 1.97 m/s.

(b) The tension in the rod at the lowest point is 1.29 N since the ball is weightless at that instant.

(c) The angle at which the tension in the rod equals the weight of the ball is 81.4 degrees.

(d) The answer to (c) remains the same if the mass of the ball is increased.

(a) To find the speed of the ball at its lowest point, we can use the conservation of energy. At the highest point, the ball has potential energy equal to mgh, where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s²), and h is the height of the ball above its lowest point. At the lowest point, all of this potential energy is converted into kinetic energy, so we can set mgh = (1/2)mv², where v is the speed of the ball at its lowest point.

Solving for v, we get:

mgh = (1/2)mv²

v² = 2gh

v = √(2gh)

Plugging in the values, we get:

v = √(2 x 9.81 x 0.62) = 1.97 m/s

Therefore, the speed of the ball at its lowest point is 1.97 m/s.

(b) To find the tension in the rod at the lowest point, we can use Newton's second law. At the lowest point, the ball is moving in a circular path with a constant speed, so the net force on the ball is the centripetal force:

F_net = mv²/r

where r is the length of the rod. The only force acting on the ball at the lowest point is tension in the rod, so we can write:

T - mg = mv²/r

Solving for T, we get:

T = mv²/r + mg

Plugging in the values, we get:

T = (0.092 kg) x (1.97 m/s)² / 0.62 m + (0.092 kg) x (9.81 m/²) = 1.29 N

Therefore, the tension in the rod at the lowest point is 1.29 N.

(c) To find the angle at which the tension in the rod equals the weight of the ball, we can use trigonometry. Let θ be the angle between the rod and the vertical. At this angle, the tension in the rod is equal to the weight of the ball, so we can write:

T = mg sin(θ)

where m is the mass of the ball and g is the acceleration due to gravity.

Solving for θ, we get:

θ = \(sin^{(-1)\)T/mg)

Plugging in the values, we get:

θ = \(sin^{(-1)\)(1.29 N / (0.092 kg x 9.81 m/s²)) = 81.4 degrees

Therefore, the angle at which the tension in the rod equals the weight of the ball is 81.4 degrees.

(d) If the mass of the ball is increased, the answer to (c) will remain the same. This is because the tension in the rod and the weight of the ball both increase by the same factor, so their ratio remains the same.

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Given that the mass of the car is m = 2000 kg and initial speed u = 20 m/s.

Here, three values of time are given.

(a) t1 = 10 s

(b) t2 = 4 s

(c) t3 = 1.2 s

In all three cases, the final velocity vis zero.

Impulse = change in momentum

= mv-mu

If the time duration is increased then force will be decreased as

Force will be lowest for 10s and greatest for 1.2 s.

The impulse will be the same for all three cases as the change in momentum is the same.

Answer:

A

Explanation:

When you dropping the swing, it increases the kinetic energy. In the middle, that is when it is at it's fullest potential. As it makes its way up, it pushes again the gravitational force, and soon, the swing will stop at the top for a VERY SHORT AND SMALL period of time. That is when it is at it's very weakest point, making the answer, indeed, A.

This is a defective question. It was WRITTEN by someone who is unclear on the concepts.  DON'T try and answer it.

It's trying to get us to use Newton's second law ... F = m • a.

But that only tells us how much force must act ON THE CAR in order to accelerate it. (45 kg) • (4 m/s^2) = 180 newtons.

This is NOT the force exerted BY the car when it hits something. THAT force depends on its speed WHEN it hits, AND how long it takes for the wreckage to actually come to rest, AND how hard or soft the wall is.

DON'T try to answer this question. Your answer will be wrong, you won't understand why, and the teacher you try to argue with probably won't either.

============================================

More explanation:

Think about jumping off of a ladder in your back yard.  Several times.

Your mass is the same every time.  Your acceleration is the same every time . . . 9.8 m/s² down, the acceleration of Earth gravity, every time.

BUT ...

-- I'll bet you would rather land on wood than on concrete. The force of landing would be less.

-- I'll bet you would rather land on dirt than on wood. The force of landing would be less.

-- I'll bet you would rather land on grass than on dirt. The force of landing would be less.

-- I'll bet you would rather land on a pile of blankets than on dirt. The force of landing would be less.

-- I'll bet you would rather land on a trampoline than on a pile of blankets. The force of landing would be less.

-- I'll bet you would rather jump from a short ladder than from a tall one.  Your speed would be less when you landed, and the force of landing would be less.

==> Your mass is the SAME every time, and your acceleration is the SAME every time.  But the force when you hit is DIFFERENT every time.

The mass and acceleration of the car DON'T tell us the force of the hit when the car hits a wall.  

Answer:

extension = 0.9 m

Explanation:

The formula relating force to extension for a spring is given as follows:

\(\boxed{F = kx}\),

where:

• F = force applied on spring

• k = spring constant

• x = extension of spring

From the above formula:

\(\frac{F}{x} = k = \mathrm{constant}\)

This means that, for a spring, the ratio \(\frac{F}{k}\) is a constant value. Therefore, we can say:

\(\frac{F_1}{x_1} = \frac{F_2}{x_2}\)

Substituting 2.0N and 0.30m for F₁ and x₁ respectively, and 6N for F₂, in the above equation, we can solve for x₂:

\(\frac{2.0}{0.3} = \frac{6.0}{x_2}\)

⇒ \(x_2 \times \frac{2.0}{0.3} = 6.0\)          [Multiplying both sides of the equation by x₂]

⇒ \(x_2 = 6.0 \div \frac{2.0}{0.3}\)

⇒ \(x_2= \bf 0.9 m\)

Therefore, the extension of the spring when 6N force is applied is 0.9 m.

The extension of the spring when the force applied becomes 6 N is 0.9 m.

The force constant or spring constant of the spring is calculated as follows;

F = kx

k = F/x

where;

k = (2 N) / (0.3 m) = 6.67 N/m

The extension of the spring when the force applied on the spring becomes 6 N is calculated as follows;

x = F/k

x = (6 N) / (6.67 N/m)

x = 0.9 m

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Answer:

Explanation:

The momentum of an object can be found by using the formula

momentum = mass × velocity

From the question we have

momentum = 78 × 24

We have the final answer as

Hope this helps you

False, Fiber optic cable is thinner and lighter than unshielded twisted pair (UTP) cable.

Fiber optic cables are made up of strands of glass or plastic fibers that transmit data through light pulses. They are immune to electromagnetic interference and can transmit signals over longer distances than UTP cables, which are made up of copper wires.The content loaded Fiber optic cable is used in high-speed internet connections because it can transmit large amounts of data at very high speeds. Additionally, fiber optic cables are more secure than UTP cables because they are much more difficult to tap into without being detected. Therefore, the statement that fiber optic cable is thicker and heavier than UTP cable is false.

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Answer: A watt unit is equal to 1 joule/sec.

Explanation:  So you have a lightbulb with 50% efficiency, so it turns half the energy it consumes into light energy.

5 answers

Answer:

 oil floats in water due to the fact that it is less dense. since the water is more dense, it is basically heavier, and heavier items always sink, while lighter items float, the same can be said about liquids. denser liquids will sink while less dense items will float.

Answer:

1.Your friend says "no thanks" to the dinner your dad cooked and prefers to just hang out with friends instead.

2. Your teammates keep making fun of you for spending so much time studying for Friday's math test.

3. Your coworkers spend every weekend watching movies at Tim's house and invite you to join them.

4. Your friends all sign up for a free class at the gym and suggest you sign up for it, too.

The change of kinetic energy is -156.7 joules.

\(V1_{i}\) =15

\(V2_{i}\)= -13.5(as towards left)

V= common velocity during collision

On applying momentum conservation during the collision

\(m_{1}V1_{i} + m_{2}V2_{i} = V ( m_{1} + m_{2})\)

\(0.650 \ 15 + 0.950 \ (-13.5) = (0.625 + 0.950) \ V\)

    \(\frac{3.075}{1.6}\) =V

V= -1.92 m/s        

To kind change in kinetic energy we will subtract final and initial kinetic energy

ΔK=\(\frac{1\ (m_{1} + m_{2} ) \ V}{2} ^{2}\) - \(\frac{1\ (m_{1} ) \ V1_{i} }{2} ^{2}\)  -  \(\frac{1\ (m_{2} ) \ V2_{i} }{2} ^{2}\)

ΔK= \(\frac{1\ (0.625 + 0.950 ) \ (-13.5)}{2} ^{2}\) -  \(\frac{1\ (0.625 ) \ 15 }{2} ^{2}\)-  \(\frac{1\ (0.950 ) \ 13.5 }{2} ^{2}\)

ΔK=   = - 156.7 J

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The fly has an average velocity of

v[ave] = ∆x/∆t = (-5.80 m) / (4.22 s) ≈ -1.37 m/s

If its acceleration is constant, then its average velocity is also equal to the average of its initial and final velocities,

v[ave] = (v[initial] + v[final]) / 2

which tells us that

v[initial] ≈ -1.37 m/s - 1/2 v[final]

The fly's final velocity after some time t is given by

v[final] = v[initial] + (-1.33 m/s²) t

so that after 4.22 s, we have

v[final] ≈ v[initial] - 5.61 m/s

Substitute this into the equation for v[initial] :

v[initial] ≈ -1.37 m/s - 1/2 (v[initial] - 5.61 m/s)

Solve for v[initial] :

3/2 v[initial] ≈ -1.37 m/s + 1/2 (5.61 m/s)

⇒   v[initial] ≈ 0.955 m/s

Two from each oxygen atom. For examples of covalent bonding are water (H2O), and carbon dioxide (CO2). Covalent compounds are mostly gases or liquids with low melting points.

Answer:

An engine made of heat!

Okay actual answer, A heat engine is a mechanical energy converter that transforms heat or thermal energy to mechanical energy.

Answer:

A solution is always transparent, light passes through with no scattering from solute particles which are molecule in size. ... A colloid is intermediate between a solution and a suspension. While a suspension will separate out a colloid will not. Colloids can be distinguished from solutions using the Tyndall effect.

Explanation:

When a suspension is allowed to stand, the particles separate. A colloid is a substance that exists between a solution and a suspension. A colloid will not separate from a suspension. The Tyndall effect can be used to distinguish colloids from solutions.

In chemistry, a suspension is a heterogeneous mixture of a fluid containing solid particles large enough to settle.

A suspension is a complex blend in which the solute particles do not disintegrate but rather become suspended throughout the bulk of the solvent and float freely in the medium.

A solution is a uniform mixture of one or more dissolved solutes in a solvent.

A solvent is a substance that dissolves a solute to produce a homogeneous mixture. The substance that dissolves in a solvent to form a homogeneous mixture is referred to as a solute.

A colloid is a mixture in which one substance is suspended throughout another, consisting of microscopically dispersed insoluble particles.

Larger particles in a suspension settle out, block or scatter light, and can be filtered out.

A colloid contains particles that are between the sizes of a solution and a colloid; they are not heavy enough to settle or be filtered out, but they still scatter light.

Thus, this way these three are related.

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Answer:

The temperature at which the Kelvin scale reading is double the Fahrenheit reading is 176.69 F = 353.38 K

Explanation:

K = 2F

→ 2F = 273 + (5/9)(F - 32)

→ 18F = 2457 + 5F - 160

→ 18F - 5F = 2457 - 160

→ 13F = 2297

→ F = 2297/13

→ F = 176.69° F

K = 2F

→K = 2 * 176.69

→ K = 353.38K

The phase difference between voltage and current in a resistive circuit is zero, while in a capacitive circuit, the voltage leads the current by 90°, and in an inductive circuit, the voltage lags the current by 90°.

In a resistive circuit, the voltage and current are in phase, meaning they reach their peak values at the same time and have zero phase difference. This is because resistors do not store or release energy and only dissipate it in the form of heat.

In a capacitive circuit, the voltage leads the current by 90 degrees. This is because a capacitor stores energy in an electric field and takes some time to charge and discharge. When an alternating current is applied, the voltage across the capacitor reaches its maximum value before the current reaches its peak. Therefore, the voltage leads the current by a quarter of a cycle or 90 degrees.

In an inductive circuit, the voltage lags the current by 90 degrees. Inductors store energy in a magnetic field, and when an alternating current flows through an inductor, the magnetic field builds up and collapses. As a result, the voltage across the inductor reaches its maximum value after the current reaches its peak. This phase delay causes the voltage to lag the current by 90 degrees.

In summary, the phase difference between voltage and current is zero in a resistive circuit, 90 degrees in a capacitive circuit (voltage leading), and 90 degrees in an inductive circuit (voltage lagging).

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la característica de los elementos

Column 1: 17.1, 17.2, 16.9, 17.3 Column 2: 16.8, 16.7, 16.6, 16.8 Column 3: 17.5, 17.2, 17.8, 17.4 Column 4: 16.9, 16.8, 17.1, 16.7

The column that shows high precision and low accuracy is Column 3.

Precision refers to the consistency and repeatability of measurements. In this case, Column 3 has measurements that are relatively close to each other, with values of 17.5, 17.2, 17.8, and 17.4. The range of these measurements is relatively small, indicating high precision.

Accuracy, on the other hand, refers to how close the measurements are to the actual value. The actual value given is 17.0. Looking at Column 3, none of the measurements match the actual value. The closest measurement is 17.2, but it is still 0.2 units away from the actual value.

Based on the given data, Column 3 exhibits high precision because the measurements are relatively close to each other. However, it shows low accuracy as none of the measurements match the actual value of 17.0.

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Answer:

rotational kinetic energy

angular momentum

the mechanical energy of frictionless systems

Explanation:

The quantities that are conserved in a movement are extremely useful for the simple resolution of different situations, in addition to the linear movement in the angular movement, some quantities are also conserved.

rotational kinetic energy

angular momentum

the mechanical energy of frictionless systems

Answer:

Should be 145854.24J or:

145.9 KJ

Explanation:

I did the calculations

During free fall, an object is subject to the force of gravity and its acceleration is equal to the acceleration due to gravity (g), which is approximately 9.81 meters per second squared (m/s²) near the surface of the Earth.

If an object is flying upward during free fall, its acceleration will still be equal to -9.81 m/s² (note the negative sign indicating that the acceleration is downward). This is because the direction of the acceleration due to gravity is always toward the center of the Earth.

Even if an object is moving upward, it is still subject to the gravitational force, which causes it to decelerate until it reaches its highest point and then starts to fall back down.

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Answer:

Downwards

Explanation:

Using Fleming's right hand rule, where the middle finger represents the negative charge moving in the south to north direction, the fore finger represents the magnetic field which points in the east to west direction.

If we are to follow this orientation and place the thumb, middle finger and fore-finger at right angles to each other, the thumb represents the direction of the magnetic force on the charge.

In this case, the magnetic force points downwards after setting the other orientations of the magnetic field and the negative charge's direction.

Answer:

First of all, what is acceleration? — Acceleration is the rate of change of velocity per unit of time.

Now, we know that velocity is a vector quantity i.e we need both magnitude and direction to define it and so is acceleration. We can now say that in acceleration, the direction of motion is very important or to define acceleration we need both the magnitude of motion (here it is the speed) and its direction.

Now coming to your question. There are two possible answers to this question.

more

,Case 2 — When the body is not moving in a straight line or is constantly changing its direction. In this cas the speed still is constant but the direction is constantly changing, for example in the case of a circular motion the direction of motion constantly changes (the direction of a moving body in a circular path at any point is the direction of the tangent of the circle at that point). Hence the velocity changes as the body move along the circular or curved path.

Now, as  I earlier mentioned to define acceleration we need to know it's magnitude and it's direction, and acceleration is the rate of change of velocity per unit of time — the speed remaining constant the direction constantly changing, and the velocity changes at different time intervals or rate of change of velocity is ≠ 0 unlike in case 1. Since there is the of and a change in velocity (speed constant but the direction is changing) there is some acceleration.

To sum everything up — in the case of linear motion i.e motion in a straight line when the speed is constant and direction is not changing, velocity will be zero and hence acceleration would be zero. In case of a non-linear motion i.e motion not in a straight line, in a circle or any path where the speed is constant but the direction is constantly changing, velocity will not be zero and hence the acceleration would not be equal to zero. Either it would be greater or less than zero.

Answer:

Hold the balloon (negatively charged) just above your head so your hair (positively charged) will be attracted to it and stand up on end. ... The can will start to roll towards the balloon without touching it. The negatively charged balloon repels the electrons of the can so that a positive charge is near the balloon.

Explanation:

I gave my explanation along with the answer.

Answer: The motions shifts.

The rating of a branch circuit is determined by its ampacity.

Ampacity is the maximum amount of electric current that a conductor or device can carry without overheating and damaging the insulation or conductors. The rating of a branch circuit is the maximum current that the circuit can safely carry without exceeding its capacity or causing damage.

This rating is typically determined by the size of the wire and the protective devices, such as fuses or circuit breakers, that are installed to prevent overloads and short circuits. Branch circuits are commonly used to power individual rooms or devices, such as outlets, lighting fixtures, and appliances. The ampacity of the branch circuit must be carefully calculated to ensure that it can handle the expected load and prevent the risk of electrical hazards.

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The rating of a branch circuit is determined by its design capacity to safely carry current expressed in terms of amperes. This prevents overheating or fire hazards. The total current flowing into a junction is equal to the total current flowing out, according to Kirchhoff's junction rule.

The rating of a branch circuit is chiefly determined by the amount of current it's designed to safely carry without overheating or causing a fire. This value is typically found in terms of amperes (or amps), which represent the unit of electrical current. An electrical appliance's requirement for operating is usually expressed in amps. Circuit breakers and fuses are also rated in amps and are designed to interrupt the circuit if the current exceeds their rated value for a specific period.

For measuring the current flowing through a branch, we use an instrument called an ammeter. It needs to be placed in series with the branch circuit, and it has a small resistance to limit its effect on the circuit.

In applications of Kirchhoff's first rule (the junction rule), each branch's current is labelled, and the direction it's going must be determined. However, the total current or the sum of the electric current flowing into and out of the junction (or point in the circuit where conductors meet) must be equal, according to the junction rule.

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About 4.5 mol of water will be created when the platinum-based engine is run continuously at 300 K for an hour with 0.5 atm of H2 and 0.5 atm of O2 injected for each reaction.

For fuel cell engines' electrodes, platinum is a requirement. It acts as an electrocatalyst to speed up the electrochemical reactions needed to induce H2 to release electrons and form H2 ions when it is placed on porous electrodes.

Platinum is particularly well suited as a fuel cell catalyst because it makes it possible for the hydrogen and oxygen reactions to occur at an ideal rate and because it is stable enough to withstand both the intense electrical current density and the complex chemical environment found inside a fuel cell. This allows platinum to function effectively over an extended period of time.

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The time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.

The cooling law is given by:

$$\frac{dQ}{dt}=-k(T-T_0)$$

where Q is the heat in the object, t is the time taken, T is the temperature of the object at time t, T0 is the temperature of the environment and k is a constant known as the cooling constant.

We need to find the time it takes for the coffee to reach a drinking temperature of 73°C given that its initial temperature is 93°C.

Therefore, we need to find the time it takes for the coffee to cool down from 93°C to 73°C when placed in a room temperature of 18°C.

Let’s assume that the heat energy that is lost by the coffee is equal to the heat energy gained by the environment. We can express this as:

dQ = - dQ where dQ is the heat energy gained by the environment.

We can substitute dQ with C(T-T0) where C is the specific heat capacity of the object.

We can rearrange the equation as follows:

$$-\frac{dQ}{dt}=k(T-T_0)$$

$$-\frac{d}{dt}C(T-T_0)=k(T-T_0)$$

$$\frac{d}{dt}T=-k(T-T_0)$$

The differential equation above can be solved using separation of variables as follows:

$$\frac{d}{dt}\ln(T-T_0)=-k$$

$$\ln(T-T_0)=-kt+c_1$$

$$T-T_0=e^{-kt+c_1}$$

$$T=T_0+Ce^{-kt}$$

where C = e^(c1).

We can now use the values given to find the specific value of C which is the temperature difference when t=0, that is, the temperature difference between the initial temperature of the coffee and the room temperature.

$$T=T_0+Ce^{-kt}$$

$$73=18+C\cdot e^{-0.09t}$$

$$55=C\cdot e^{-0.09t}$$

$$C=55e^{0.09t}$$

$$T=18+55e^{0.09t}$$

We can now solve for the value of t when T=93 as follows:

$$93=18+55e^{0.09t}$$

$$e^{0.09t}=\frac{93-18}{55}$$

$$e^{0.09t}=1.3636$$

$$t=\frac{\ln(1.3636)}{0.09}$$

Using a calculator, we can find that the time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.

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