To practice Problem-Solving Strategy 7.1 Rotational dynamics problems.
Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the angular acceleration when it has an angle of 10.0 degreesfrom the vertical?
Sort the forces as producing a torque of positive, negative, or zero magnitude about the rotational axis identified in Part A. Keep in mind that counterclockwise rotations are positive.

The momentum during the collision is conserved. Hence, the total initial momentum is equal to the total final momentum. Therefore, the initial velocity of the car with a mass of 3250 Kg was, 2.05 m/s.

Momentum of a body is the product of its mass and velocity. Momentum is a vector quantity having both magnitude and direction.

The momentum during a collision is conserved. Thus,the sum of initial momentum of the colliding  bodies is equal to the final momentum of the combined mass.

Given that, mass of car 1 = 2150 Kg

velocity = 10 m/s

Momentum = mass × velocity.

= 10 m/s × 2150 Kg = 21500 kg m/s.

Mass of car 2 = 3250 kg

the combined mass = 3250  + 2150 = 5400 Kg

final velocity = 5.22 m/s

final velocity = 5400 Kg × 5.22 = 28188 kg m/s .

momentum of car 1 + momentum of car 2 = 281888 kg m/s

21500 kg m/s + (3400 Kg × V) = 281888 kg m/s

v = 2.05 m/s.

Therefore, the initial velocity of the car with a mass of 3250 Kg is 2.05 kg m/s.

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Your question is incomplete. But your complete question probably was:

A 2150 kg car, moving east at 10.0 m/s, collides and joins with a 3250 kg car. The cars move east together at 5.22 m/s. What was the initial speed of car with 3250 kg mass.

(i)The time can be calculated using the equation:

\(d=v0t+1/2\)\(gt^{2}\)

\(v = 0 + 9.8 * 3.19 = 31.3 m/s\)\(t = sqrt(2d/g) = sqrt(2 * 50 / 9.8) = sqrt(10.2) = 3.19s\)

So the velocity of the car at the bottom of the hill is 31.3 m/s.

(ii)To find the height at which the car will have half this speed,

\(v = v0 + gt\)

\(t = (v - v0) / g = (15.65 - 0) / 9.8 = 1.59 s\)

\(d = v0t + (1/2)gt^2\)

where d is the distance traveled, v0 is the initial velocity

\(d = 0 * 1.59 + (1/2) * 9.8 * 1.59^2 = 12.1 m\)

So the car will have half the velocity at the bottom of the hill when it is 12.1 m below the top of the hill.

When an object moves under the influence of gravity, it experiences a constant acceleration due to gravity, which is approximately 9.8 m/\(s^{2}\) on the surface of the Earth.

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Answer:

(b) A convex mirror can form a magnified real image.

Explanation:

A convex mirror only forms diminished/highly diminished, virtual and erect image.

Hope it helps.

Answer:

A. Piccolo

B. The flute would usually have the highest pitch, but because the piccolo is half the size of a flute, it's higher pitched. The piccolo in C has a range from D5 – C8 which is pretty high pitched. This means that the piccolo's range is an octave above that of the flute.

C. The human ear naturally picks out higher notes, so when piccolos play extremely high, we can hear them more easily than the other instruments in a band or orchestra.

D. I'm sorry but I don't know this one.

Answer:

Sh = Vh t         horizontal distance traveled

Sh = 10.2 m/s * 3.7 s = 37.74 m

1. The x component of the force is 4.4 N

2. The y component of the force is 3.5 N

The following data were obtained from the question:

1. How to determine the x component

x component = FCosθ

x component = 5.6 × Cos 39

x component = 4.4 N

2. How to determine the y component

y component = FSineθ

y component = 5.6 × Sine 39

y component = 3.5 N

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The mass of gas particles is a factor that affects gas pressure. As the mass of the gas particles increases, the force exerted by them increases as well, resulting in higher gas pressure. However, as the number of particles in a given volume of gas is constant, the more massive the particles, the fewer there will be in that volume, resulting in a decrease in the pressure.

The gas particle's mass plays a significant role in determining the pressure of the gas. The pressure of a gas is defined as the force applied to a unit area. Because gas particles are in constant random motion, they collide with each other and the container's walls, exerting a force on them. The force exerted by the gas particles is determined by the frequency and magnitude of these collisions, as well as the particles' mass.
As the mass of the gas particles increases, so does their momentum. This implies that the gas particles collide with the container walls with greater force, resulting in a higher gas pressure. However, as the number of particles in a given volume of gas is constant, the more massive the particles, the fewer there will be in that volume, resulting in a decrease in the pressure.
The relationship between the mass of the gas particles and the gas pressure can be illustrated using the kinetic theory of gases. According to this theory, the pressure of a gas is directly proportional to the number of particles in a given volume, the average kinetic energy of the particles, and the volume. The mass of the particles is not explicitly included in this equation. However, the average kinetic energy of the particles, which is proportional to the square root of their mass, is a key factor in determining the pressure.

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a)The aperture size of the radio telescope needs to be approximately 0.27 meters b)The aperture of a radio telescope needs to be much larger than that of an optical telescope because radio waves have much longer wavelengths compared to visible light. c)the resolving power of a telescope depends on the ratio of the wavelength of light.

a. To determine the aperture size of a radio telescope to achieve a resolution at 21 cm, we can use the Rayleigh criterion, which states that the minimum resolvable separation (δθ) is given by:

δθ = 1.22 * (λ / D)

Where λ is the wavelength of the radiation and D is the diameter of the telescope's aperture.

Given that the radio wavelength is 21 cm (or 0.21 m), and we want to achieve the same resolution as the optical telescope (1 second of arc), we can rearrange the formula to solve for D:

D = 1.22 * (λ / δθ)

D = 1.22 * (0.21 m / 1 second of arc)

Calculating the result:

D ≈ 0.27 m

Therefore, the aperture size of the radio telescope needs to be approximately 0.27 meters to achieve a resolution of 1 second of arc at a wavelength of 21 cm.

b. The Rayleigh criterion tells us that the resolution of an instrument is inversely proportional to the wavelength.

Since radio waves have longer wavelengths, the telescope's aperture needs to be larger to achieve the same resolution as an optical telescope. This is because a larger aperture collects more incoming waves and allows for finer spatial detail to be resolved.

c. The ability to resolve two objects using a telescope depends on the size of the aperture relative to the wavelength of the radiation. When it comes to resolving stars, the resolving power of a telescope depends on the ratio of the wavelength of light to the size of the telescope's aperture (λ/D).

Blue light has a shorter wavelength compared to red light. Since the resolving power is directly proportional to the wavelength, a shorter wavelength of blue light allows for better resolution.

Therefore, two predominantly blue stars can be resolved because their shorter wavelength allows for finer detail to be distinguished, while the same separation between two predominantly red stars cannot be resolved due to the longer wavelength.

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Complete question:

A hydraulic jack is used to lift a car by applying a force of 120N at the pump piston, if the area of the ram and pump piston are 100cm squared and 1m squared respectively. What is the weight of the car?

Answer:

the weight of the car is 1.2 N

Explanation:

Given;

applied force, F₁ = 120 N

area of the effort (pump), A₁ = 1 m²

area of the load (ram), A₂ = 100 cm² = 1 x 10⁻² m²

let the weight of the car = F₂

The applied pressure is constant and the following equations can be used to calculate the weight of the car.

\(P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \\\\F_2 = \frac{F_1 \times A_2}{A_1} \\\\F_2 = \frac{120 \times (1\times 10^{-2})}{1} \\\\F_2 = 1.2 \ N\)

Therefore, the weight of the car is 1.2 N

Answer:

standard

Explanation:

we sometimes use weights of known mass to balance with an object of unknown mass to determine that objects weight.

The weight of a 52 kg astronaut in space at constant velocity would be zero. This is because weight is the force exerted on an object due to gravity, and in space, there is no gravity acting on the astronaut. Therefore, the astronaut's weight would be zero.

To calculate weight, we use the formula:

Weight = Mass × Acceleration due to gravity In space, the acceleration due to gravity is zero, so the formula becomes:

Weight = Mass × 0 Weight = 0

So even though the astronaut has a mass of 52 kg, their weight in space at constant velocity would be zero. It is important to note that weight and mass are not the same thing. Mass is a measure of the amount of matter in an object, while weight is the force exerted on an object due to gravity.

This is why an astronaut's mass remains the same in space, but their weight becomes zero. In conclusion, the weight of a 52 kg astronaut in space at constant velocity is zero. This is because there is no gravity acting on the astronaut in space, so the force exerted on them due to gravity is zero.

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Answer:

Newton's second law states that force is directly proportional to the product of mass and acceleration.

so if you hit a baseball with a bat it will accelerate according to the applied force.

The correct statement is:

O It can increase the distance over which output force acts by applying less output force than input force.

Machines can make work easier by trading off force for distance. For instance, by extending the distance across which the force is delivered, a lever can be utilized to raise a heavy object with less force.

The short end of the lever receives the input force, and the long end receives the output force. Although it functions across a wider area, the output force is smaller than the input force. This makes it easier for the user to lift the bulky object.

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The speed of the 12 g bullet is approximately 509.19 m/s when it causes the 11 kg stationary wood block to slide 4.2 cm across the table, with a coefficient of kinetic friction (μk) of 0.20. To find the speed of the 12 g bullet, we will use the conservation of momentum and the work-energy principle. Here are the steps to find the bullet's speed:

1. The total initial momentum of the system (bullet + wood block) is equal to the total final momentum of the system, since there are no external forces acting in the horizontal direction.
Initial momentum = Final momentum
m_bullet * v_bullet = (m_bullet + m_block) * v_final
2. To find the final velocity (v_final) of the system, we will use the work-energy principle.
Work done by friction = Change in kinetic energy
μk * m_block * g * d = 0.5 * (m_bullet + m_block) * v_final^2

3. Rearrange the equation from step 2 to find v_final.
v_final^2 = (2 * μk * m_block * g * d) / (m_bullet + m_block)
v_final = √((2 * μk * m_block * g * d) / (m_bullet + m_block))
4. Plug in the given values (converting grams and cm to kg and m respectively) and solve for v_final.
v_final = √((2 * 0.20 * 11 kg * 9.81 m/s^2 * 0.042 m) / (0.012 kg + 11 kg))
v_final = 0.553 m/s
5. Use the momentum conservation equation from step 1 to solve for v_bullet.
0.012 kg * v_bullet = (0.012 kg + 11 kg) * 0.553 m/s
v_bullet = (11.012 kg * 0.553 m/s) / 0.012 kg
v_bullet =509.19 m/s. So the speed of the bullet is 509.19 m/s.

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Most red galaxies, which are often elliptical galaxies, can be found in the red sequence. Most blue galaxies, the majority of which are spirals, are found in the blue cloud in Magnitude-color diagram.

The green valley, which contains some red spirals, is a sparsely populated area that lies between the two distributions. Magnitude-color diagram of the galaxy Three populations are shown in this fictitious galaxy Magnitude-color diagram: the red sequence, the blue cloud, and the green valley. The absolute magnitude (a metric of luminosity) and mass of galaxies are related, as seen by the galaxy color-magnitude diagram.

The absolute magnitude (a metric of luminosity) and mass of galaxies are related, as seen by the galaxy color-magnitude diagram. Eric, provided a preliminary explanation of the three sections of this graphic in 2003.

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The rock concert is approximately 1,000,000 times greater in terms of sound pressure level.

The decibel (dB) is a unit used to measure sound pressure level (SPL) or loudness. A difference of 10 dB represents a ten-fold increase in sound pressure level, which corresponds to a perceived doubling of loudness.

A typical rock concert has an SPL of 110 dB, which is 60 dB greater than a normal conversation at 50 dB. To find the ratio of the two SPLs, we can use the formula:

Ratio = 10^(difference in dB/10)

Substituting the values, we get:

Ratio = 10^(60/10) = 10^6 = 1,000,000

So, the SPL of a typical rock concert is 1 million times greater than the SPL of a normal conversation.

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Answer:

Its A

Explanation:

Create the Android App, set up the project, design the user interface, handle user input, perform calculations, and display the results.

Creating an Android App that calculates force and density can be done by following these steps:

Set up the project in Android Studio.

Design the layout of the user interface using XML, including TextViews, EditTexts, and a Button.

Define the necessary variables and views in the Java code.

Set an onClickListener for the button to perform the calculations.

Retrieve the user input from the EditText fields and convert them to appropriate data types.

Calculate the force using the formula F = ma and the entered mass and acceleration.

Display the calculated force in the result TextView.

Repeat steps 5-7 for calculating density if desired.

Run the app on an Android emulator or device to test its functionality.

The Simplifying User Input App developed in class can serve as a guide for implementing the user interface and handling user input.

You would need to modify the code to incorporate the force and density calculations based on the provided equations.

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Answer:

c

3 half lifes have passed to get to 1/8

1/2 then 1/4 then 1/8

so 15*3

Explanation:

The sandbag will hit the ground with a velocity of -48 feet per second (negative sign indicates the downward direction).

(a) To determine the time it takes for the sandbag to strike the ground, we can use the equation:

h(t) = h₀ + v₀t + 0.5at²

where h(t) is the height at time t, h₀ is the initial height (64 feet), v₀ is the initial velocity (16 ft/s), a is the acceleration (-32 ft/s²), and t is the time in seconds. We want to find the time t when h(t) = 0 (when the bag hits the ground).

0 = 64 + 16t - 16t²
0 = 64 - 16t²

Now, we solve for t:

t² = 4
t = 2 seconds

The sandbag will strike the ground 2 seconds after its release.

(b) To find the velocity at which the bag hits the ground, we use the equation:

v(t) = v₀ + at

where v(t) is the velocity at time t, v₀ is the initial velocity (16 ft/s), a is the acceleration (-32 ft/s²), and t is the time in seconds.

v(2) = 16 - 32(2)
v(2) = 16 - 64
v(2) = -48 ft/s

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Answer:

the weight is different on the moon

Explanation:

Answer:

Explanation:

Formula

KE = 1/2 m v^3

Givens

m  = 54 kg

v = 30 m/s

Solution

KE = 1/2 54 * 30^2

KE = 1/2 54 * 900

KE = 27 * 900

KE = 24300 Joules

Answer:

fridge microwave washer dryer tv fan dishwasher fish tank lights toaster coffee pot

Answer:

Acceleration.

Explanation:

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.

Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

\(Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}\)

\(a = \frac{v - u}{t}\)

Where,

a is acceleration measured in \(ms^{-2}\)

v and u is final and initial velocity respectively, measured in \(ms^{-1}\)

t is time measured in seconds.

The S.I unit for measuring acceleration is meters per seconds square (m/s²).

Hence, 10 m/s^2 is an example of acceleration.

If you build a common-source amplifier with an NMOS input transistor, and you want a current source as a load, and that current source goes from VDD to a node, the type of current source would be the diode-connected transistor.

An NMOS current source implemented as a diode-connected transistor is a type of bipolar transistor circuit that creates a constant current from an input voltage. The collector and emitter of the bipolar transistor are connected together in the circuit, effectively turning the transistor into a diode. The main advantage of diode-connected transistors is that they can generate currents of a specific magnitude and not be influenced by changes in the supply voltage.

The current generated by the diode-connected transistor is almost completely determined by the physical characteristics of the transistor and the biasing resistors used in the circuit. Another advantage of diode-connected transistors is that they may be cascaded in series to create current sources of various sizes. These devices have been commonly used to generate reference currents, voltage-to-current (V-I) converters, and bias currents in linear integrated circuits. So therefore diode-connected transistor is the type of current source, if you build a common-source amplifier with an NMOS input transistor, and you want a current source as a load, and that current source goes from VDD to a node.

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When a certain shade of blue has a frequency of 7.33×10¹⁴ Hz. So, the energy will be 4.86×10⁻¹⁹ J,

To calculate the energy of one photon of a certain shade of blue light with a frequency of 7.33×10¹⁴ Hz, we can use the formula: E = hf, where E is the energy of one photon, h is Planck's constant, and f is the frequency of the light.

Using Planck's constant ℎ=6.626×10⁻³⁴ J⋅s, we can calculate the energy of one photon of the blue light as follows:

E = hf = (6.626×10⁻³⁴ J⋅s)(7.33×10¹⁴ Hz) = 4.86×10⁻¹⁹ J

Therefore, the energy of exactly one photon of this light is 4.86×10⁻¹⁹ J.

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Answer:

Speed is a scalar quantity, that is, it is a number and indicates how fast (or slow) one travels at any given time.

Velocity is a vector quantity, this means that it has magnitude and direction, that is, how fast an object travels and its where its going (speed + the direction in which the object moves).

Acceleration is the ratio of the velocity change over the time interval in which this velocity change occurred. Acceleration as well as velocity is a vector quantity so it is made up of magnitude and direction.

The differences between these three quantities are important for the description of the movement. In the case of speed and velocity, its difference lies in the fact that velocity indicates the direction in which the movement is taking place (and speed is only a number), which in many physical phenomena the direction of movement is an important property. And the difference between acceleration and velocity is that acceleration instead of a velocity indicates a change in velocity (either in magnitude, direction or both), which tells us how fast a velocity will increase or decrease over time.