when a 2.5 g penny is placed on a turntable rotating at 33 rpm (revolutions per minute), it is found that the farthest away from the center of the turntable that it can be located without slipping off is 10 cm. what is the coefficient of static friction between the penny and the surface of the turntable?

The equation for the density is D = m/v.

Density is the substance's mass consistent with the unit of quantity. The symbol most customarily used for density is ρ, despite the fact that the Latin letter D can also be used. Density is the size of ways tightly a cloth is packed together. it's far defined as the mass consistent with unit quantity.

ρ = m/V, wherein ρ is the density, m is the mass of the item and V is the quantity of the object.

The density of a liquid is a measure of how heavy it is for the quantity measured. in case you weigh the same amounts or volumes of two one-of-a-kind beverages, the liquid that weighs extra is greater dense.

The density is of two types, one is absolute density, and the alternative is relative density. Relative density is also called unique gravity, which is the ratio of the density of a material to the density of a reference material. typically, the reference fabric is water.

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Using the concepts of impulse, we got that   8.8Nsec is the the magnitude of the impulse delivered to the baseball by the bat when a batter applies an average force of 8000 n to a baseball for 1. 1 ms.

In classical mechanics, impulse (symbolized by J or Imp) is  integral of a force, F, over the time interval, t, for which it acts. Since force is the vector quantity, impulse is also a vector quantity. Impulse applied to the object produces the equivalent vector change in its linear momentum, also in the resultant direction.

We know very well that impulse is given by =Force × Time

 We have magnitude of force is 8000Newton and time is 1ms which is equivalent to (1/1000)sec.

Therefore, impulse value is =Force × Time

             =>impulse=8000×(1.1)×(1/1000)

             =>impulse=8×1.1

              =>impulse=8.8Nsec

Hence, when A batter applies an average force of 8000 n to a baseball for 1. 1 ms, the magnitude of the impulse delivered to the baseball by the bat is 8.8Nsec.

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Inside the doppler impact,  elements that have an effect on the frequency of sound waves consist of; the speed of the source and the velocity of the observer.

The rate of alternate inside the function of an object in any route. velocity is measured because of the ratio of distance to the time in which the space became covered. speed is a scalar amount because it has the handiest route and no importance.

Speed can be the notion of the rate at which an item covers distance. A short-shifting object has a excessive velocity and covers a substantially huge distance in a given amount of time, even as a gradual-moving item covers a relatively small amount of distance in the equal amount of time.

The primary unit or the S.I. unit of speed is m/s or ms⁻¹.

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This model represents how electromagnetic radiation transmits energy and it shows: C. an electric field and a magnetic field vibrating perpendicular to each other.

In Science, an electromagnetic energy can be defined as form of energy that is primarily carried by electromagnetic waves such as:

This ultimately implies that, an electromagnetic energy simply refers to a form of energy that typically moves as particles at the speed of light, which is about three hundred million meters per seconds (3 × 10⁸ m/s) and they are always perpendicular to each other.

Based on the model shown in the image attached below, we can logically deduce that a single light wave travels away from a source within an electric field and a magnetic field that are vibrating perpendicular to each other.

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A 2.0-kilogram cart traveling at a constant speed in a horizontal circle of radius 3.0 meters. The magnitude of the centripetal force of the cart is 24 newtons. The speed of the car is 6 m/s. Thus, Option A is the correct answer.

To find the speed, the given values are,

Mass m = 2 Kg

Radius r =3 meters

Centripetal force = 24 Newtons.

A centripetal force is the force which is made up of two Latin words centrum which means center and peterum which means to seek.

It is defined a force which make a body to follow a curved path. The direction of this force is always orthogonal to the body's motion and it is always towards the fixed point which is instantaneous center of the path's curvature.

Centripetal force is expressed according to the formula;

F = mv²/r

m is the mass of the body

v is the speed of the cart

r is the radius

Substituting the values into the formula and get v,

24 = 2v²/3

24×3 = 2v²

72 = 2v²

v² = 72/2

v² = 36

v =√36

v = 6m/s

Hence, the speed of the cart is 6m/s. Thus, Option A is the correct answer.

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The centripetal force on the model helicopter is 6.25N.

The radius of the curve of the model helicopter is 30m and the mass of the helicopter is 300g, it is travelling with a speed of 90km/h.

Converting the speed into m/s, speed is 25m/s.

The centripetal force on a body is given by,

F = Mv²/r

Where,

F is the force,

V is the speed,

r is the radius,

So, putting values for helicopter,

F = 0.3 x 25 x 25/30

F = 6.25 N.

So, the centripetal force is 6.25 N.

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The net force acting on a 1.0-kg ball moving at a constant velocity will be zero

Since , ball is moving at a constant velocity , that means there is no acceleration as acceleration is equal to change in velocity divided by time . Here velocity is constant hence no change in velocity is taking place .

since, there exist no acceleration which means there exist no external force . Hence , net force on the ball is zero in this system .

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Answer:

See below

Explanation:

Velocity is how fast an object is moving....acceleration is how fast the velocity is changing .

Answer:Since Mercury's period is 88 days (page 182), the period of this hypothetical planet would be 0.354 ´ 88 = 31 days

Explanation: I hope this is correct

The prices of the different units of volume and mass of mercury are as follows as the Price of one pound of mercury = $2.059

The price of the intermediate volumes of Mercury are determined as follows:Price of 1 g of mercury = $0.00454, Price of 1 cm³ of mercury = $0.0614 and Price of 1 in³ of mercury is $0.996 and Price of 1 g of mercury = $0.00454, Price of 1 cm³ of mercury = $0.0614 and Price of 1 in³ of mercury is $0.996

b. 1 pound = 453.592 g

76 pounds = 76 * 453.592 g = 34473 gPrice of 1 g of mercury = $156.50/34473 Price of 1 g of mercury = $0.00454

Volume of 34473 g of mercury = 34473/13.534

Volume of 34473 g of mercury = 2547.14 cm³

Price of 1 cm³ of mercury = $156.50/2547.14 cm³

Price of 1 cm³ of mercury = $0.0614 Price of 1 in³ of mercury:

1 cm³ = 0.0610 in³

2547.14 cm³ = 2547.14 * 0.0610 in³

2547.14 cm³ = 157.02 in³

Price of 1 in³ of mercury = 156.5/157.02

Price of 1 in³ of mercury = $0.996

In conclusion, the prices of the different units of volume and mass of mercury are found by conversion.

Therefore, Mercury has an orbital period of about 88 Earth days.

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The elevator accelerates with an acceleration of a=-2.45 m/s2 in a downward direction.

Any vector's magnitude, represented by its unit and pointing in the direction of the vector, is its length. As a result, the acceleration's magnitude is equal to the length of the acceleration vector and it is pointed in the same direction. For any vector quantity, this is true.

Three situations can be distinguished when figuring out the direction of acceleration: when picking up speed, the acceleration is in the direction of movement; when slowing down, the acceleration is in the opposite direction to the direction of movement; and when driving around a corner at a constant speed, the acceleration is in the direction of movement.

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Answer: It decreases because of air resistance.

Explanation:

If the gap between them doubles, the gravitational pull will be reduced to one-fourth of its current strength.

The force is smaller the further apart the masses are. The gravitational force does not decrease by half when the distance between two masses is doubled because it is proportional to 1/d2, but rather by 1/4.

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The direction of the magnetic force on the loop is going inside the loop. If the loop place on the paper, the magnetic force going through the paper.

If a loop of wire is electrified there will be a uniform magnetic field. We use the right-hand rule for loops to calculate the direction of the magnetic field. The rules are

Imagine a loop on paper. A clockwise current on the loop, curl your fingers, and go in a clockwise direction.

Your thumb gonna points down and the magnetic force going inside the paper.

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The rotational speed is 5.8 rad/s.

This is a rotational system related to rotational motion and the system is made up of the merry-go-round and the child, for which we write the moment of two instants

Initial

        L₀ = I₀ w₀

Final

         L_{f} = I w

        L₀ = L_{f}

        I₀ w₀ = I_{f} w

        .w = I₀/I_{f}   w₀

The initial moment of inertia is

       I₀ = 0.0011 kg. m2

The final moment of inertia

       l_{f}  = 0.0011 + m r²

        I_{f} = 0.0011 + (43) (1.5)²

        I_{f} = 4160.25 kg m²

Initial angular velocity

        w₀ = 0.22 rad / s

Let's calculate

        rotational speed = (0.0011/4160) 0.22

        rotational speed = 5.81 rad / s

Therefore, the rotational speed when the child arrives at center is 5.81 rad/s.

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The final speed of the joined cars after the collision as stated in the question is; [tex]v_f[/tex] = (v/2)√(5 - 4sin ϕ)

From the law of conservation of linear momentum, we know that;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where;

m₁ = mass of car 1

u₁ = Initial velocity of Car 1

m₂ = mass of car 2

u₂ = initial velocity of car 2

v₁ = final velocity of car 1

v₂ = final velocity of car 2

We are told that before the collision, one car was traveling in the northern direction while the second car was traveling in the southeastern direction at an angle ϕ.

We are given the initial speed of the first car = 2v.

Thus;

The horizontal component of the initial velocity of the first car; u₁ₓ = 0

The vertical component of the initial velocity of the first car; u₁y = 2v j^

Similarly, for the second car, we are given initial speed = v

Thus;

The horizontal component of the initial velocity of 2nd car; u₂ₓ = v cos ϕ

Vertical component of initial velocity of first car; u₂y = v sin ϕ (-j^)

Since both of their masses are m, after collision since they travel together, their combined masses will be 2m.

They now move together in a northeastern direction at an angle θ.

Thus, resolving the final velocities gives us;

vₓ = [tex]v_f[/tex]sin θ (i^)

[tex]v_y[/tex] = [tex]v_f[/tex] cos θ (j^)

Thus, along the x-axis, we now have;

m₁u₁ₓ + m₂u₂ₓ = 2mvₓ

Plugging in the relevant values, we have;

m(0) + m(v cos ϕ) = 2m([tex]v_f[/tex] sin θ (i^))

v cos ϕ = 2(v_f sin θ (i^))  ---(eq 1)

Similarly, along the y-axis, we have;

m(2v j^) + m(v sin ϕ (-j^)) = 2m([tex]v_f[/tex] cos θ (j^))

⇒ 2v - v sin ϕ = 2v_f cos θ   ---(eq 2)

We will square both eq 1 and eq 2 and add to each other to get;

v² cos² ϕ + (2v - v sin ϕ)² = 4([tex]v_f[/tex])² (sin²θ  + cos²θ)

⇒ v² cos² ϕ + (2v - v sin ϕ)² = 4([tex]v_f[/tex])²

⇒ v² cos² ϕ + 4v² - 4v² sin ϕ + v²sin²ϕ = 4([tex]v_f[/tex])²

⇒ v²(cos² ϕ + sin²ϕ) + 4v² - 4v² sin ϕ = 4([tex]v_f[/tex])²

cos² ϕ + sin²ϕ = 1. Thus;

⇒ v² + 4v² - 4v² sin ϕ = 4([tex]v_f[/tex])²

⇒ 5v² - 4v² sin ϕ = 4([tex]v_f[/tex])²

[tex]v_f[/tex] = (v/2)√(5 - 4sin ϕ)

Velocity is the direction in which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea

A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in meters per second (m/s or m/s1) in the SI (metric system). In contrast to "5 meters per second east," which is a vector, "5 meters per second," for instance, is a scalar.

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By adding the time of flight at the top of the cliff and the time taken down the hill, the ball spent 2.72 s of time in air.

A projectile can be a stone or a ball or any object that can be projected. The object projected will take a trajectory path.

Given that acceleration due to gravity is 9.8 m/s and a 0.87 kg projectile is fired into the air from the top of a 8.52 m cliff above a valley. Its initial velocity is 9.1 m/s at 49◦ above the horizontal. To know how long the projectile will be in the air, we will calculate the total time of flight at the top of the cliff and the time taken down the hill

Time of flight T = 2usinФ/g

Where

Substitute all the necessary parameters into the formula

T = (2 × 9.1sin49)/ 9.8

T = 13.74/9.8

T = 1.40 s

The time taken down the cliff can be found with formula

h = ut + 1/2gt²

where u = 0

8.52 = 0 + 1/2 × 9.8 × t²

8.52 = 4.9t²

t² = 8.52/4.9

t² = 1.738

t = √1.738

t = 1.32 s

Time for the projectile in the air = T + t

Time in air = 1.40 + 1.32

Time = 2.72 s

Therefore, the projectile will be in the air for 2.72 seconds long.

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The amount of time is the independent variable, while the water phase change is the dependent variable.

The independent variable is any variable in the experiment that does not change along the experiment but whose values are associated with the modification in the dependent variable (such as in this case time to observe water phase change).

Therefore, with this data, we can see that the independent variable does not change along the experimental procedure and is known to be the cause of the change in the dependent variable.

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Answer:

(A)    conduction implies that the objects are in contact

There are two forces at play in a tug of war. The force produced by stretching the rope is indeed called tension. This power drives these people forward.

Another force acting on them is the friction of the soles of the feet. In tug-of-war, if two teams exert the same force on the rope, the net force on the rope is zero, so the rope stays in the same place. A rope has zero tension when both ends of the rope are pulled by two opposing forces of 100 N each. This is because both forces have the same magnitude but act in opposite directions on the same object and cancel each other out.

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Answer:

the acceleration of an object is directly related to the mass of the object

The linear acceleration is 82.45 m/sec².

Linear acceleration is described as uniform acceleration because of a transferring body in a straight line. There are three equations that are essential in linear acceleration relying upon the parameters like initial and final pace, displacement, time, and acceleration.

Whilst linear acceleration is implemented to a frame, the whole body is affected by the acceleration (or the force) at the same time. Fee of exchange in pace consistent with unit of time even as on an instant route. that is linear acceleration. Angular acceleration is the rotational acceleration felt by using an object on approximately an axis.

Calculation:-

Given,

diameter = 0.70 m

                = 0.3

The angular acceleration = 2π (280 - 130)/4

                                           = 235.575

linear acceleration = r × 235.575.

                                 = 0.35 × 235.575.

                                 = 82.45 m/sec²

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The initial volume can be calculated using Charles's law. The initial volume of the ammonia gas was 770 cm³.

According to Charles's law, at constant pressure, the volume and temperature of a gas is directly proportional. Thus, v/t = a constant.

V1/T1 = V2/ T2

Given that the final volume and temperature are 731 cm³ and -14 degree Celsius or 269 K respectively. Thus the volume of the gas at 0 degree Celsius or 273 K is :

volume  V1 = V2 T1 / T2

                   = (273 K × 731 cm³ ) /269 K

                   =  770 cm³.

Thus, the initial volume of the gas was 770 cm³.

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Answer:

[tex] \Huge{\boxed{84 N}} [/tex]

Explanation:

The amount of force required here can be found by using the formula

where

mass is in kg

acceleration in m/s²

From the question

mass = 4 kg

acceleration= 21 m/s²

We have

force = 4 × 21 = 84

We have the final answer as

Total distance travelled by an athlete is approx 4 km.

We have given following information, let the total distance travelled by an anthlete be x km

An athlete runs first part of total distance (x) with a velocity 12 km/ h for 4 minutes.

the next part of x km is travelled by an anthlete with 14 km/h for 4 minutes.

one other part of x km is travelled by an anthlete with 19 km/h for 5 minutes

Change the time units from minutes to hours

1 hour = 60 min => 4 minutes = 4/60 h = 1/15 h

and 5 minutes = 1/12 h

Now use the velocity formula ,

velocity = distance/ time

=> distance = velocity × time

so, total distance (x ) = 12 km/h × 1/15 h + 14 km/h × 1/15 h + 19 km/h × 1/12 h = (12/15 + 14/15 + 19/12)

= 3.91 km ~ 4 km

therefore, total distance travelled by an anthelete is 4km.

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dolphin traveled after 2 h is equal to 6 km .

What is velocity ?

Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.

Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). An object is said to be accelerating if its velocity, direction, or both change.

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Answer:

Explanation:

The moon is held in its orbit around Earth by gravity. The moon also feels a gravitational pull from the sun. Which of the following is true?

According to Newton's third law, the interaction forces are the same.

(a) The force of the moon acting on the sun is equal to the force of the sun acting on the moon.

Answer:

A

Explanation:

Potential energy = m g h       unless h changes there is zero PE change

To known the motion and horizontal velocity.

What is motion?

In physics, motion changes over time depending on a body's position or orientation. Translation is the action of moving along a line or curve. Rotation is the term used to describe motion that modifies a body's orientation.

What is horizontal velocity?

The speed of a projectile is constant in the horizontal plane.Gravity causes a vertical acceleration that is 9.8 m/s/s downward. Each second, a projectile's vertical velocity changes by 9.8 m/s, A projectile's horizontal motion exists independently of its vertical motion.

If we perform an experimented see that the only force acting on the projectile is the gravity which acts vertically (neglecting air resistance). The component of gravitational force along horizontal direction is zero. Thus, there is no force acting horizontally acceleration in horizontal direction is zero.

Therefore, velocity in horizontal direction remains constant.

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Find the wire tension is true or not.

What is tension?

The force transmitted through a rope, string, or wire when it is pulled by forces acting from opposite sides is referred to as tension. The bodies at each end of the wire are subjected to an equal amount of tension force that is applied along the entire length of the wire.

What is force?

The force that a rope, cord, or other similar object applies to an object is known as the force of tension. Horizontally, two walls are separated by a thin wire. What holds true about the tension T in the wire if a weight W is suspended from it? It is impossible to establish the connection between T and W.

Therefore, it is impossible to establish the connection between T and W.

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Work done by the piston is 421.40 J

Work is the energy transferred to or from an object by applying a force along a displacement. In its simplest form, if the constant force is aligned with the direction of travel, it equals the product of the force and the distance traveled.

The formula for calculating the work done is:

W = -P × ΔV

P = pressure

ΔV = change in volume

Substitute the values in the formula:

W = -P × ΔV

W = -8 × (0.65 - 0.13)

W = -8 × 0.52

W = -4.16 atm L

1 atm L = 101.3 J

-4.16 atm L = -4.16 × 101.3 J

= 421.40 J

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