problem 4: a disk of mass m and radius r, a hoop of mass 2m and radius r, and a ball of mass m and radius 2r are rolling without slipping. the hoop can be treated as a thin ring and the ball should be modeled as a hollow sphere.

a) The acceleration magnitudes of the sled is 0.62 m/s². b) The acceleration magnitudes of the girl is 0.13m/s². c) The distance from the girl is 2.6m.

(a) The girl's force is the sole horizontal force acting on the sled because friction is insignificant. The total of the vertical forces—gravitational force and the normal force of the ice—is zero. The sled accelerates with an acceleration of

a s = F/m s = 52N/8.4kg = 0.62m/s².

​(b) The third law of Newton states that the force exerted by the sled on the girl is 5.2N. Her acceleration is equal to a g times m g.

​a s= F/m s = 5.2N/40kg = 0.13m/s².

(c) The sled and girl are accelerating in the opposite directions. The coordinate for the girl, assuming she starts at the origin and advances in the +x direction, is given by x g = 2 1 a g t 2. The sled moves in the -x direction and begins at x 0 = 15m. Its location is indicated by the coordinates x s =x 0 2 1 a s t 2. They collide when x g = x s, or when 2 1 a g t 2 = x 0 2 1 a s t 2.

When this occurs

t= a \sg \s​ \s +a \ss \s​

2x \s0

​The girl has already traveled the distance x g = 2 1 a s t 2 = a g + a s by that point.

​x \s0 \s​ \s a \sg

​​ \s = \s0.13m/s \s2 \s +0.62m/s \s2

(15m)(0.13m/s \s2 \s ) \s​ \s =2.6m

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The magnitude of the second charge is 3.01 x 10⁻⁵C.

The second charge is positive.

The magnitude of the second charge is determined by applying Coulomb's law of electrostatic force as shown below.

F = kq₁q₂/r²

where;

Substitute the given parameters, and solve for the magnitude of the second charge as shown below.

q₂ = Fr²/kq₁

q₂ = (65 x 0.5²) / (9 x 10⁹ x 6 x 10⁻⁵)

q₂ = 3.01 x 10⁻⁵C

Thus, the magnitude of the second charge is 3.01 x 10⁻⁵C. Also, since the force is attractive, the second charge must be positive.

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5.45 second  it will take for the grinding wheel to stop an electric motor rotating a workshop grinding wheel at a rate of 103 rev/min is switched off with a constant deceleration of 1.96 rad/s 2

ω1 = 2π(103/60) = 10.7 rad/s

ω2 = 0

α = -1.96 rad/s^2

time t = (ω2 - ω1)/α

= 10.7  / 1.96

= 5.45s

θ = ω1t + (1/2)αt^2

 = 58.31 - 29.12 = 29.21

Generally speaking, deceleration is a decrease in acceleration. When an object's speed decreases with respect to time, it is said to be decelerating. In contrast to acceleration, deceleration involves a negative rate of change in velocity.

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The time it takes for the water along the shore to go from high to low and back again is six hours and 12.5 minutes between high tides, which happen every twelve hours and twenty-five minutes.

How long does it take for the tide to change from high to low?

six days, twelve and five minutes

Coastal locations see two high and two low tides every 24 hours and 50 minutes because the Earth spins through two tidal "bulges" every lunar day. There are 12 hours and 25 minutes between high tides. The sea level at the shore can change from high to low or from low to high in six hours and 12.5 minutes.

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The acceleration vector will be the vector sum of the tangential and radial acceleration components because the train is changing both its speed and direction.

Since the train is altering both its speed and direction, the vector sum of the tangential and radial acceleration components will represent the acceleration vector.

The radius of curve and the train's speed can be used to calculate the tangential acceleration, while the elapsed time and changing speed can be used to calculate the radial acceleration.

Let's first convert the speed measurements from km/h to m/s:

v I = 90.0 km/h

= (90.0 km/h) (10 3 m/km) (1 hour and 36 minutes)

= 25.0

m/s v f = 50.0 km/h

= (50.0 km/h) (10 3 m/km) (1 hour and 36 minutes)

= 13.9 m/s

Backwards, the tangential acceleration is equal to a t = t v = 15.0s (13.9 m/s 25.0 m/s = 0.741 m/s 2), and the radial acceleration is equal to a r = r v 2.

Consequently, an is equal to 1.48 m/s 2 inward and 29.9 0 backward.

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The gas that makes up this layer is Ozone.

The ozone layer protects the earth from most of the sun's UVB rays. Greenhouse gases are a set of gases that accumulate in the lower layer of the atmosphere, the troposphere and absorb infrared radiation to increase the average temperature of the Earth's surface. At the top of the stratosphere, 30 miles up, ozone absorbs most of the sun's harmful UV rays.

At the top of the troposphere 12 miles up, ozone acts as a greenhouse gas and traps heat. The troposphere is the lowest layer of the Earth's atmosphere. Most of the atmospheric mass is in the troposphere. Most types of clouds are in the troposphere, and almost all weather phenomena occur in this layer. Ozone protects the earth's surface from ultraviolet radiation from the sun. The ozone layer reduces the risk of skin cancer.

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The ranking  in order from largest to smallest of the magnitudes of the horizontal forces f1 , f2 , and f3 acting on the arrows is F1=F2=F3>0 because there is no change in the horizontal motion of the arrows.

All three arrows in the scenario have been shot and it is assumed that air resistance can be neglected. With the motion of the arrows in horizontal direction, there is no likely change in the horizontal motion of the three arrows. This makes the three forces equivalent to one another and each force is equal to zero (i.e. F1=F2=F3=0).

Here's the complete question:

Rank in order, from largest to smallest, the magnitudes of the horizontal forces F1, F2, and F3 acting on the arrows. Some may be equal. State your reasoning. Rank in order, from largest to smallest, the magnitudes of the horizontal forces , , and acting on the arrows. Some may be equal. State your reasoning.

a. F3>F1=F2 because the mass of the first arrow is equal to the mass of the second arrow which is less than the mass of the third arrow.

b. F1=F2=F3=0 because there is no change in the horizontal motion of the arrows.

c. F1>F2=F3 because the velocity of the second arrow is equal to the velocity of the third arrow which is less than the velocity of the first arrow.

d. F1=F2=F3>0 because there is no change in the horizontal motion of the arrows.

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If the first runner wants to stay side-by-side with the second runner, The angular velocity needs to be the same as they would then cover equal angular distance for a period of time.

An equal angular distance means that it would always be side to side.In order to do this, the first runner needs to run at a faster speed than the second runner. This is because the second runner is running in a larger circle than the first runner, so she covers more ground in the same amount of time. The first runner needs to make up for this by running at a faster speed.

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The maximum static friction that could be exerted on the crate is 58.8.

Static friction is a force that keeps an object at rest. Friction is experienced when individuals try to move a stationary object on a surface, without actually triggering any relative motion between the body and the surface on which it is on.

Formula for static friction:

Static friction(max) = Normal force × Static friction

= mg × μ

m = mass = 10kg

g = gravity on the body = 9.8 m/s²

μ = static friction = 0.60

Now putting these values in the equation, we get:

Static friction = 10 × 9.8 × 0.60

                     = 58.8

Therefore the static friction is 58.8.

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The force exerted on each of its edges  at the given shear stress and area is determined as 2.8 x 10¹⁰ N.

The force exerted on each plate is calculated by applying the formula for shear stress as shown below.

Shear stress is the force that tends to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Like the name implies, shear stress or forces tends to "shear" object or cause deformation of materials.

F = Aσ

where;

Substitute the given parameters and solve for the force applied to create the shear stress.

F = (0.8 m²) x (3.5 x 10¹⁰ Pa)

F = 2.8 x 10¹⁰ N

Thus, the force exerted on each of its edges resulting in the given displacement increases as the shear stress increases.

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The direction is the force that the bed exerts on the crate Forward.

Friction between the track and the crate holds the crate in place and allows the crate to move with the vehicle. As a result, the crate's frictional force is directed north, in the same direction as the truck's velocity. As mentioned earlier, both the horizontal and vertical forces have a magnitude of 0 so there is no net force on the box. Therefore, the force on the box has no direction.

The net force always has the same direction as the acceleration. For an object in a circular motion with constant velocity, the net force is directed toward the center of the circle around which the object is moving. The frictional force acts on a moving object, and its direction is opposite to the direction of movement. As we walk, our feet are pushed backward so friction works in the opposite direction to counteract the push.

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When air expands it is warm outside then the air is contracted and becomes cool.

The atmosphere of Earth or also known as air is the layer of gases retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere.

When warm air expand,  the molecules heat and move faster makin them to move apart. So we know that air expands when heated and contracts when cooled, the reason for that is because there is more space between the molecules, the air is less dense than the surrounding matter and the hot air floats upward.

Atmospheric convection helps us to understand that as air heats up and becomes less dense, it rises higher into the air. As it reaches higher elevations, it encounters less air pressure. The lower air pressure at higher elevations allows the air to expand even more. As this air continues to expand, it begins to cool down.

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Given,

The distance covered by the football, d=30 m

The time it takes for the football to cover the given distance, t=2.5 s

The speed of an object is given by the ratio of the distance covered by the object to the time it takes for the object to cover that distance.

Thus the speed of the ball is given by,

On substituting the known values in the above equation,

Thus the speed of the ball is 12 m/s

Therefore the correct answer is option B.

Explanation:

intensity, direction, color, contrast, hardness

The change in temperature in kelvin, given that the system was heated from 5 °C to 10 °C is 278 K

We'll begin by obtaining the change in temperature in degree Celsius. This can be obtained as follow:

ΔT = T₂ – T₁

ΔT = 10 – 5

ΔT = 5 °C

Finally, we shall convert 5 °C to unit in kelvin. This can be obtained as follow:

T(K) = T(°C) + 273

T(K) = 5 + 273

T(K) = 278 K

Thus, from the above calculation, we can conclude that the change in temperature is 278 K

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An increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass. It depends on the object's mass and acceleration due to gravity.

Mass is an intrinsic unchanging property. Weight is a force and it depends on gravitational force. This force is directly proportional to mass the more mass the object has the stronger the force of gravity will be. Because of this, it turns out that gravity does not matter when we compare the distance traveled by objects with different masses. The important part of the force is air resistance also called drag.

The slope of the graph is the relationship between weight and mass. The slope tells how many newtons of weight pull down on each kilogram of mass. Mass is the measure of the amount of matter in an object. This is an immutable property inherent in the body. Mass cannot be destroyed or created. Weight is the production of mass and acceleration due to gravity.

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Answer:

T² ∝ r³

Answer:

Vy = V0 * sin θ          vertical speed

Vy = 30 m/s * sin 29 = 14.5 m/s

t = 14.5 m/s / 9.8 m/s^2 = 1.48 sec         time to reach max height

H = Vy t - 1/2 g t^2       acceleration is in opposite direction to initial Vy

H = 14.5 m/s * 1.48 s - 1/2 * 9.8 m/s^2 * (1.48 s)^2

H = 10.7 m

The potential energy and kinetic energy are constantly changing because of law of energy conservation as the kinetic energy is constantly being converted into potential energy and vice versa.

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

The total mechanical energy of any system is made up of kinetic energy and potential energy.

The kinetic energy is the energy of the object due to its motion while the potential energy is the energy of the object due to its height above the ground.

Based on the law of conservation of energy, the kinetic energy of an object can be converted into potential energy and from potential energy to kinetic energy.

Thus, the potential energy and kinetic energy are constantly changing because of law of energy conservation as the kinetic energy is constantly being converted into potential energy and vice versa.

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25 Newton is the average net force on the small boat during the 20s period

initial velocity of boat=0.5m/s

after t= 20s, velocity of boat= -2m/s

acceleration of boat=

[tex]a=v-u/t=-2-0.5/20[/tex]

[tex]a=-0.125m/s^2[/tex]

total weight= 200 kg

average net force= ma

average net force=200×0.125

average net force=25N

In mechanics, a force is any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three principles of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the idea of force (1687).

Newton's first law states that unless a force is applied to a body, it will stay in either its resting or uniformly moving condition along a straight path. According to the second law, when an external force applies on a body, the body accelerates (changes velocity) in the force's direction.

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mg x sin A calculates the force pushing the mass down the hill. Additionally, this force has the same formula: m x a, where an is the actual acceleration in the plane. By dividing the difference between the two speeds by the provided time, or 5.07 m/s - 1.31 m/s / 1.73 s = 4.34 m/s2, the acceleration a may be calculated.

Ma is therefore equal to mg times sin A, or sin A = a / g, or 4.34 m/s2 times 9.81 m/s2 times 0.439.

A = arc sin(0.439)sin(26.0) =

Friction is a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, such the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.

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Answer:OB=58.3m

Explanation:

So here cow wanders 30m in north and turns 22 degrees in right side and moves 40m more, as shown in figure given.

now take the starting point as a origin such that cow moves in x-y co-ordinate axis.

As shown in figure length OA is the length when cow moves in north or y direction. Later she takes 22 degrees turn to right and moves 40m more.

So the final displacement is the length of cow from the origin that is length OB.

now co-ordinates of B are [40cos22°,40sin22°+30] i.e [37.084,44.984]

now displacement of cow= length of OB

                                           = [tex]\sqrt{[37.084]^{2}+[44.984]^{2} }[/tex]

                                           =[tex]\sqrt{3398.78}[/tex]

                                     OB =[tex]58.3[/tex]

ANSWER:

Sphere B

STEP-BY-STEP EXPLANATION:

The time of the air depends on the mass, initial velocity and the height of the object, having the same mass and the same height, it depends only on the initial velocity.

The higher the initial velocity, the shorter the time in the air, therefore in this case the sphere B that has a lower velocity will be the one that will spend the longest time in the air.

density   ρ=mass/volume  density accuracy > 1%

cube volume  = 27 cm^3&mass = 140.4 g Density =140.4/27=5.2g/cm^3 sphere volume = 12 cm^3&mass= 61.6 g Density =61.6/12=0.133g/cm^3

mass per unit volume of a solid substance; density. Density is defined as d = M/V, where M stands for mass, and V for volume. The unit of density that is most frequently used is grammes per cubic centimetre. For instance, the density of Earth is 5.51 grammes per cubic centimetre, while the density of water is 1 gramme per cubic centimetre. Kg per cubic metre is another way to measure density (in metre-kilogram-second or SI units). Air, for instance, has a density of 1.2 kilogrammes per cubic metre. Books and manuals list the densities of typical solids, liquids, and gases. An easy way to determine a body's mass from its volume, or vice versa, is by its density.

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Answer: a=.347

Explanation: Acceleration can be calculated by subtracting the initial velocity (2.1 m/s) from the final velocity (7.3) and dividing the difference by the time (15s).

[tex]\frac{7.3-2.1}{15} = .347[/tex]

The angle of refraction for the light ray with the wavelength of 589nm traveling through air strikes a crown glass at 30.0° incidence is 19.2°.

Refraction is the quantity used to measure the amount of refraction taking place at any boundary when light passes between the two mediums.

Refractive index can be calculated using Snell's law, the formula for calculating angle of refraction is as follows:

n₁/n₂ = sinФ₁/sinФ₂

n₁. sin(i) = n₂. sin(r)

where, n₁ = refractive index of medium 1

n₂ = refractive index of medium 2

i = angle of incidence in air

r = angle of refraction in glass

Therefore, by putting the values in this formula we can get the angle of refraction.

(1) × sin(30°)=(1.52) × sin(r)

sin(r)= 1/2 × 1.52

sin(r) = 1/ 3.04

r = sin⁻¹(0.328)

r = 19.2°

Therefore, Angle of refraction = 19.2°

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Your question is incomplete, most probably the complete question is:

A light ray of wavelength 589 nm (produced by a sodium lamp) traveling through air strikes a smooth, flat slab of crown glass at an angle of 30.0 to the normal. If the index of refraction of the crown glass is 1.52 and the index of refraction of air is 1. Find the angle of refraction.

The Potential energy is 2450 J.

Potential energy = mgh

m = mass of an object

g = acceleration due to gravity

h =  height of an object where it is placed

Put these values in formula, mgh

Potential energy = mgh

Potential energy = 50×9.8×5

Potential energy = 2450 J

Potential energy is stored energy in an object. Potential energy is the product of mass of an object, acceleration due to gravity and height of an object where it is placed.

The S.I. unit of potential energy is joule and is represented by J.

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The correct answer is option D: halved

Energy becomes half i.e. E' = E/2 if the distance between the plates is doubled.

Let's say the area of parallel plates = A

The distance between plates = d

The potential difference between Plates = V

Now, the capacitance is given by

C = ∈[tex]o[/tex] A / d

If the separation between the plates is doubled then the value of capacitance will become half.

C' = ∈[tex]o[/tex] A / 2d

C' = C/2

Now, we can determine the electrical energy stored in the capacitor which is given by

E = [tex]\frac{1}{2}[/tex] [tex]CV^{2}[/tex]

When the distance between the plates is doubled then energy becomes

E' = [tex]\frac{1}{2}[/tex] x [tex]\frac{C}{2}[/tex] x [tex]V^{2}[/tex]

E' = E/2

Thus, energy becomes half i.e. E' = E/2 if the distance between the plates is doubled.

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The complete question is:

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference V across the plates. If the separation between the plates is doubled, the electrical energy stored in the capacitor will be: _______

a- doubled

b- unchanged

c- quadrupled

d- quartered

e- halved