State Newton's First law of motion.

Answer:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Explanation:

it's newton's second law

Answer:

B is the correct answer

Explanation:

just bc I said so:)

To produce a force of 12 kN in the press, a tangential turning force of 1187500 N (1187.5 kN) must be applied to the wheel.

Force is an influence that causes a change in the motion, shape, or both of an object. It is the result of an interaction between two objects, and is described through Newton's three laws of motion. These laws explain the relationship between force, mass, and acceleration.

The pitch of the screw is the distance between two adjacent threads on the screw, and is 0.20 cm in this case. The wheel diameter is 55 cm.

To calculate the force needed to produce a force of 12 kN in the press, we use the following equation: F = (12000 N * 55 cm) / (0.20 cm * 0.4).

This equation takes into account the pitch of the screw, the wheel diameter, and the efficiency of the press.

Plugging in the numbers, we get: F = (12000 N * 55 cm) / (0.20 cm * 0.4) = 1187500 N.

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Answer:

convection currents

Explanation:

Answer:

2.00x 10 14th Hz

Explanation:

Answer:

2.99 x 10^14 Hz

Explanation:

E photon= hf (you have to solve for f)

f= E photon/h

f= 1.98 x 10^-19 J / 6.63 x 10^-34 J x s

f=2.99 x 10^14 Hz

A. The time taken for the stunt man to hit the mattress is 1.75 s

B. The velocity the stunt man as he slams into the mattress is 17.15 m/s

h = ½gt²

15 = ½ × 9.8 × t²

15 = 4.9 × t²

Divide both side by 4.9

t² = 15 / 4.9

Take the square root of both side

t = √(15 / 4.9)

t = 1.75 s

Thus, it will take the stunt man 1.75 s to hit the mattress

v = gt

v = 9.8 × 1.75

v = 17.15 m/s

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Answer:

Explanation:

FBEDAC

Explanation:

The energy of the system before the collision must equal the energy after the collision.

After the collision the bullet and the block have a total mass of 18.41 kg and they move at a speed of 8.8 m/s. The kinetic energy after the collision is

\(\frac{18.41 kg (8.8 m/s)^2}{2} = 713 J\)

Before the collision only the bullet has kinetic energy.

So we can now determine the speed of the bullet using

\(\frac{0.11kg (v^2)}{2} = 713 J\\v = 114 m/s\)

Answer:

D

Explanation:

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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When a car collides with another object, the total momentum of the system before and after the collision must be conserved. Momentum, on the other hand, is a product of mass and velocity. To find the velocity of a car after a collision, we must first consider the initial momentum of the system before the collision and compare it to the final momentum after the collision.

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Answer:

Explanation:

4 is right

The angular displacement of the rotor in the given time is,

Substitute the known values,

The arc length traced by tip of the blade is,

Substitute the known values,

Thus, the arc length traced by the tip of blade is 20100 m.

Answer:

Yes

Explanation:

Yes, we can control the motion.

Motion can be controlled by applying friction which is a force that opposes the motion. For example, if a car is in motion, brakes are applied to stop the motion of the car, this is due to the use of force of friction to convert that kinetic energy into heat.

Hence, the correct answer is "yes".

The mass of the trailer would be 0.10 kg

The period of a mass spring system is said to be directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

It is represented thus;

T = 2π × √ m ÷ k

But note that period (T) is the reciprocal of frequency (f)

So, T = 1 ÷ f

Then, T = 2π × √ m ÷ k = 1 ÷ f

Make the mass 'm' the subject of the formula

m = k ÷ 2π^2 × f^2

Where

m = mass

k = spring constant

f = frequency

π = 3. 14

Mass, m = 1. 0 × 10^ 0 ÷ 2× 3.14 × 3.14 × 0.71 × 0. 71

= 1.0 × 1 ÷ 9. 94

= 0. 10 kg

Therefore, the mass of the trailer would be 0. 10kg.

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Answer:

S = Vo t * 1/2 a t^2     equation for distance traveled

w = w0 t + 1/2 a t^2    equivalent circular equation where w equals omega

w = 5.98 * 27.5  + a (27.5)^2/ 2

a = (w2 - w1) / t = -5.98 / 27.5 = -.217

w = 5.98 * 27.5 - 1/2 * .217 * 27.5^2 = 82.4

Since 1 Rev = 2 pi  radians      

Rev = 82.4 / 2 * pi = 13.1 Rev

Answer:

Explanation:

The potential energy of a body can be found by using the formula

PE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 9.8 m/s²

PE = 10 × 9.8 × 20

We have the final answer as

Hope this helps you

Answer:

Explanation:

The horizontal velocity is 1.61.

Answer:

\(V_2=3.3m/s\)

Explanation:

From the question we are told that:

Distance \(d_1=1.4m\)

Tangential speed \(V=2.2m/s\)

Distance 2 \(d_2=2.1m\)

Generally the equation for Angular velocity is mathematically given by

 \(w=\frac{v}{r}\)

Therefore

 \(\frac{v_1}{r_1}=\frac{v_2}{r_2}\)

 \(V_2=\frac{2.2*2.1}{1.4}\)

 \(V_2=3.3m/s\)

Answer:

A. Sulfur _________ group 16 chalcogens

B. Sodium _________ group 1 alkali metals

C. Argon _________ group 18 noble gases

D. Silicon _________ group 14 carbon family

E. Chlorine _________ group 17 halogens

F. Phosphorus_________ group 15 pnicogens

The energy that would reach the cold reservoir is  1370 J.

The efficiency of a heat engine is a measure of how much of the heat energy supplied to the engine is converted into useful work. It is defined as the ratio of the work output to the heat input, and is typically expressed as a percentage.

Efficiency = (Work output) / (Heat input) * 100%

We have to note that the energy that would reach the heat  engine is;

43/100 * 3190

= 1370 J as shown

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Answer:

A.

Position-time graph:

The position-time graph for the ball punted vertically will be a parabolic curve, with the vertex at the highest point of the ball's trajectory. Since the initial position is zero, the curve will go through the origin.

Velocity-time graph:

The velocity-time graph will be a straight line that starts at the initial velocity and decreases linearly until it reaches zero at the highest point of the ball's trajectory. After that, the velocity increases linearly in the negative direction until the ball hits the ground.

Acceleration-time graph:

The acceleration-time graph will be a constant negative value, representing the acceleration due to gravity.

Motion map:

A motion map is a diagram that shows the position of an object at several specific times during its motion. For the ball punted vertically, the motion map would look like this:

|O|------|-------|------|-------|------|H|

O represents the initial position, and H represents the highest point of the ball's trajectory. The "|" symbols represent the position of the ball at regular intervals of time.

B.

To find the initial velocity of the ball, we can use the hang time and the acceleration due to gravity.

Hang time = 3.8 seconds

Acceleration due to gravity = -9.8 m/s^2

At the highest point of the ball's trajectory, the velocity is zero. Therefore, we can use the following kinematic equation to find the initial velocity:

hang time = (final velocity - initial velocity) / acceleration

Solving for initial velocity:

initial velocity = final velocity - (hang time x acceleration)

final velocity = 0 m/s

hang time = 3.8 s

acceleration = -9.8 m/s^2

initial velocity = 0 - (3.8 x -9.8)

initial velocity = 37.64 m/s

Therefore, the initial velocity of the ball was 37.64 m/s.

Answer:

This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.

The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.

The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).

The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:

R(n) = √(X² + Y²)

Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.

However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:

<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2

<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2

Because <X²> = <Y²>, we can write:

<R²> = <X²> + <Y²> = n A²

So, the root mean square distance (the square root of the mean square displacement) after n steps is:

R(n) = √(<R²>) = √(n) * A

Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.

The magnitude and direction of the resultant of the five concurrent forces acting on a bolt is  390.58 N and -82.8 ⁰ respectively.

The magnitude and direction of the resultant of the five concurrent forces acting on a bolt is calculated as follows;

The sum of the x component of the five forces is calculated as;

F₁ₓ = -80 N x cos (27) = -71.28 N

F₂ₓ = -400 N x cos (22) = - 370.87 N

F₃ₓ = -150 N x cos (22 + 46) = -56.2 N

F₄ₓ = 300 N x cos (45) = 212.13 N

F₅ₓ = 250 N x cos (18) = 237.76 N

∑Fₓ = -48.98 N

The sum of the y component of the five forces is calculated as;

F₁y = -80 N x sin (27) = -36.32 N

F₂y = 400 N x sin (22) = 149.84 N

F₃y = 150 N x sin (22 + 46) = 139.1 N

F₄y = 300 N x sin (45) = 212.13 N

F₅y = -250 N x sin (18) = -77.25 N

∑Fy = 387.5 N

The magnitude of the resultant force;

F = √ (387.5² + 48.98²)

F = 390.58 N

The direction of the force;

θ = tan⁻¹ ( Fy / Fₓ )

θ = tan⁻¹ ( 387.5 / -48.98 )

θ = -82.8 ⁰

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Answer:

Explanation:

The acceleration of an electron in an electric field is given by the equation:

a = qE/m

where a is the acceleration, q is the charge of the electron, E is the electric field, and m is the mass of the electron.

Given that the acceleration of the electron is 4.3 m/s^2, and the mass of the electron is 9.11 × 10^-31 kg, and the charge of the electron is -1.6 × 10^-19 C, we can solve for the electric field E:

E = ma/q

E = (4.3 m/s^2) × (9.11 × 10^-31 kg) / (-1.6 × 10^-19 C)

E = -2.44 × 10^4 N/C

The negative sign indicates that the direction of the electric field is opposite to the direction of the electron's motion. Therefore, the magnitude of the electric field required to accelerate an electron with an acceleration of 4.3 m/s^2 is 2.44 × 10^4 N/C and the direction is opposite to the direction of motion of the electron.

For the following are four electrical components:

a. For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction.

For the following are four electrical components:

a. Sketches of current-voltage characteristics:

For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

  Current (I)

     ^

     |          B

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

     Current (I)

     ^

     |          A

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

For component C, a filament lamp, the current-voltage characteristic would be a curve that is not linear. It would exhibit a non-linear increase in current with increasing voltage. At lower voltages, the lamp would have low resistance, but as the voltage increases, the resistance of the filament also increases due to the phenomenon of thermal self-regulation. This leads to a slower increase in current at higher voltages.

For component D, a component that does not obey Ohm's law, the current-voltage characteristic could be any non-linear curve depending on the specific component chosen. Examples of components that do not obey Ohm's law include diodes and transistors.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it. As the voltage across the filament increases, the temperature of the filament increases as well, causing its resistance to increase. This increase in resistance results in a slower increase in current with increasing voltage, leading to the characteristic non-linear curve observed.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction. It exhibits a non-linear current-voltage characteristic where it conducts current only when the voltage is above a certain threshold, known as the forward voltage. Below this threshold, the diode has a high resistance and blocks current flow in the reverse direction. The characteristic curve of a diode would show negligible current flow until the forward voltage is reached, after which it exhibits a rapid increase in current with a relatively constant voltage.

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The formula you mentioned is known as the dot product formula or the scalar product formula. It is used to find the angle between two vectors u and v.

Let's start by defining the vectors u and v. Suppose we have two vectors u and v in a two-dimensional space.

u = (u1, u2)

v = (v1, v2)

The dot product of these vectors is defined as:

u . v = |u| |v| cos(β)

where |u| and |v| are the magnitudes of the vectors u and v respectively, and β is the angle between the vectors u and v.

Now, let's derive this formula. The dot product of two vectors u and v is given by:

u . v = (u1 × v1) + (u2 × v2)

The magnitude of a vector is given by:

|u| = sqrt(u1² + u2²)

|v| = sqrt(v1² + v2²)

We can use the dot product and magnitude equations to obtain:

cos(β) = (u . v) / (|u| × |v|)

Multiplying both sides by |u| × |v| gives us:

|u| × |v| × cos(β) = u . v

Therefore, we have derived the dot product formula:

u . v = |u| × |v| × cos(β)

This formula can be used to find the angle between two vectors u and v in any two-dimensional or three-dimensional space.

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The complete question is-

Write the proof of the formula

u.v=|u||v|cosβ

Determine the magnitude of B-A is 53.68

1.4

Magnitude is a term used to describe size or distance. We can relate the magnitude of the movement to the size and movement speed of the object. The magnitude of a thing or an amount is its size. A car moves at a faster pace than a motorcycle, just in terms of speed.

Magnitude is the relative size of an object (mathematics). The mathematical term for a vector's length or size is the norm. By using the symbol |v|, the magnitude of a vector formula can be utilized to determine the length of a given vector (let's say v). This amount is essentially the distance between the vector's beginning point and ending point.

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The work done by \(\vec F\) along the given path C from A to B is given by the line integral,

\(\displaystyle \int_C \mathbf F\cdot\mathrm d\mathbf r\)

I assume the path itself is a line segment, which can be parameterized by

\(\vec r(t) = (1-t)(-2\,\vec\imath + 5\,\vec\jmath) + t(4\,\vec\imath+7\,\vec\jmath) \\\\ \vec r(t) = (6t-2)\,\vec\imath+(2t+5)\,\vec\jmath \\\\ \vec r(t) = x(t)\,\vec\imath + y(t)\,\vec\jmath\)

with 0 ≤ t ≤ 1. Then the work performed by F along C is

\(\displaystyle \int_0^1 \left(6x(t)^3\,\vec\imath-4y(t)\,\vec\jmath\right)\cdot\frac{\mathrm d}{\mathrm dt}\left[x(t)\,\vec\imath + y(t)\,\vec\jmath\right]\,\mathrm dt \\\\ = \int_0^1 (288(3t-1)^3-8(2t+5)) \,\mathrm dt = \boxed{312}\)