a mass m at the end of a massless rod of length l swings as a pendulum with two horizontal springs for negligible mass and spring constants k1 and k2 acting on it. both springs are relaxed when the rod is vertical. what is the period of small oscillations? [from feynman exercises in physics]

Answer:

Explanation:

And what to find in the problem?

The distance travelled by the block of mass m will be l₀ + x or d which can be calculated through implementing the Conservation of energy from Work energy theorem

For  l₀ + x, (from figure)

sinᶿ = h / (l₀+x) ----- equation 1

We know from conservation of energy,

Ka + Ua = Kc + Uc

Here

Ka = kinetic energy at point A

Ua = potential energy at point A

Kc = kinetic energy at point C

Uc = potential energy at point C

Since the block is at rest Ka = 0 & block comes to rest after moving Kc = 0 as well

Therefore Ua = Uc

Ua = m.g.h

Uc = ½ kx²

m.g.h = ½ kx²

h = kx²/2mg ---- equation 2

Substitute the obtained value of h i.e. equation 2 in equation 1 for calculation of distance travelled by the block on an inclined plane.

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Answer:

d = (2mg sinθ) / k

Explanation:

We can use the conservation of energy.

At the point when the block comes to rest, all of its initial potential energy mgh is converted into the potential energy stored in the spring (1/2)kx², where x is the amount by which the spring is compressed.

Using trigonometry, we can see that the height h of the incline is equal to

d sinθ

where d is the distance traveled by the block down the incline.

We know this because d represents an incline and to find the y value of an incline we use sinθ

Therefore, we can write:

mgh = (1/2)kx²

Substituting h = d sinθ and solving for d, we get:

mgd sinθ = (1/2)kd²

d = (2mgsinθ)/k

Therefore, the correct answer for the distance that the block slides down the incline before coming momentarily to rest is (2mg sinθ)/k.

I hope this helped! :)

The wire must be cut at a length of l/5 along its length so that the resistance of one piece is four times the resistance of other.

The relation between the resistance the resistivity the area and the length of the wire is given by,

R = pl/A

p is resistivity,

A is the area,

l is the length of the wire.

Let us say that the peace of length X is cut from the wire,

So, length of one piece is x and of the other is (l-x)

The resistance of the bigger price has to be four times of the other.

So, we can write,

px/A = 4p(l-x)/A

x = 4l-4x

5x = l

x = l/5.

So, the wire should be cut at a point l/5 from one of the ends of the wire.

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The speed of the ball immediately after being struck is 28.65 m/s.

Impulse is equal to momentum change when a collision happens and no external forces on the system.

I = Δp

I = p' - p

I = mv - mu

Parameter

I = mv - mu

9.97 = 0.34v - (0.34×0)

9.97 = 0.34v

[tex]v = \frac{9.97}{0.34}[/tex]

v = 28.65 m/s

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The acceleration will be 0.35 m/s^2 if he pulls with the same force when the wagon contains a child weighing 3 times of wagon.

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The resistance of the light bulb has the power of 40 W is 722.5 ohms

The power of the light bulb = 40 W

The maximum voltage of the lightbulb = 170 V

Therefore, the resistance of the light bulb can be found using the formula,

                        P = V² / R

where P is the power of the lightbulb

           V is the voltage of the lightbulb

           R is the resistance of the lightbulb.

Let us re-write the above equation in order to get the value of the resistance,

                    R = V² / P

Let us substitute the known values in the above equation, we get

                   R = (170)² / 40

                      = 28,900 / 40

                      = 722. 5 ohm

Therefore, the resistance of the light bulb is 722.5 ohms.

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The height of a hill from which the person throws a ball horizontally with a velocity of 12 m/s and the ball lands 10.1 m away from the hill is 3.47 m.

The height of a hill from which the person throws a ball horizontally with a velocity of 12 m/s and the ball lands 10.1 m away from the hill is calculated as follows;

The ball was projected horizontally from the top of a hill, therefore, there is no vertical component of the velocity of projection and the object is considered to be undergoing free fall under gravity from a height, h.

The height from which an object falls freely under gravity is calculated with the formula below:

H = gt²/2

where g is the acceleration due to gravity = 9.81 m/s²

t is time.

the time taken for the fall = horizontal distance / velocity

t = 10.1 / 12

t = 0.841 s

Therefore;

h = 9.81 * (0.841)² / 2

h = 3.47 m

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Any point in the wire has 1.12 x [tex]10^{19}[/tex]. electrons flow per second.

The current is the quantity of charge Q flowing through a certain point of the wire in a time interval of [tex]\Delta t[/tex].

I = [tex]\frac{Q}{\Delta t}[/tex].

by using this relationship

I=1.80 A, we can find the charge passing any point in the wire in 1 second:

Electric Charge, Q = 1.80 C.

To find how many electrons corresponds to this charge, we should divide this value by the charge of a single electron

charge of the electron = 1.6 x [tex]10^{-19}[/tex] C.

No. of Electrons = Q/q = [tex]\frac{1.80}{1.6* 10^{-19}}[/tex]= 1.12 x [tex]10^{19}[/tex].

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The method of radiation is faster through a vacuum, the method of convection is faster through a gas and the method of conduction is faster through a solid.

There are three modes of heat transfer:

conduction

convection, and

radiation

Radiation:

The emission of energy as electromagnetic waves or as moving subatomic particles, especially high-energy particles causes ionization. As we know vacuum does not require any medium so radiation is the heat transfer which is faster in a vacuum.

Therefore we get that in vacuum radiation, solid conduction, and gas convection heat transfer is faster.

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The additional power required to carry the plate at speed of 72 km/hr is 4867.8 m/s.

Given data,

[tex]l[/tex] (wide of plate) = 1.9m

[tex]h[/tex] (high of plate) = 0.5m

ρ (air density) = 1.22

[tex]V[/tex] (speed) = 72km/hr

assume [tex]C_{D}[/tex] (Drag coefficient) = 1.05

To determine the additional power can be calculated as follows:

First, we have to determine the area of plate

Area of plate = [tex]l[/tex]×[tex]h[/tex]

= 1.9×0.5

Then, we have to convert the unit of speed from km/hr to m/s

72km/hr = [tex]\frac{72000}{3600}[/tex]

= 20 m/s

Next, we can determine the power by using the formula

=[tex]\frac{1}{2}[/tex]×[tex]C_{D}[/tex]×ρ×[tex]V^{2}[/tex]×[tex]A[/tex]×[tex]V[/tex]

=[tex]\frac{1}{2}[/tex]×[tex]1.05[/tex]×[tex]1.22[/tex]×[tex]20^{2}[/tex]×[tex]0.95[/tex]×[tex]20[/tex]

=4867.8 watt

Thus, The additional power required to carry the plate at speed of 72 km/hr is 4867.8 m/s.

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The average momentum of the avalanche was found to be 1.3×10^ 9 kg·m/s

what is momentum?

Momentum is the pace at which a security's price accelerates—that is, the rate at which the price changes. Momentum trading is a method that uses momentum to enter a trend while it is gaining traction.

Simply expressed, momentum is the tendency of a price trend to continue growing or dropping for a set period of time, taking into consideration both price and volume data. Momentum is commonly quantified using an oscillator in technical analysis and used to help detect trends.

Momentum is the quantity of motion of an item. If you know the object's velocity and mass, you can calculate its momentum. It will be simple once you understand the formula.

The average momentum of the above problem was 1.3 x 10^9Kg.m/s

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The magnitude of the charge on the particle is 0.0083 C.

Solution:

The centripetal force if it is moving in a circle is mv^2/r. Since this is coming from the magnetic force, then

mv^2/r = qvB

q = (mv^2/r)/(vB) = (mv)/(rB)

q = .002*5/(.2*6) = 0.0083 C

The magnitude of the electric field E produced by a charged particle at a point P is the electric force per unit positive charge exerted on another charged particle at that point. The direction of the electric field is the direction of the force on the positive charge. The electric field vector magnitude is calculated as the force per charge for any testing charge in the electric field.

The force on the test charge can be directed toward the source charge or directly away from the source charge. Electron charge can be determined simply by placing a known number of electrons on one electrode of a capacitor and measuring the voltage Vs across the capacitor.

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If there is no nozzle attached and the average hose velocity is 6 ft/s, determine p. Neglect little elevation changes and losses. = 70f7.

Velocity, as opposed to speed, refers to the pace and direction of an object's movement as it moves down a path. In other words, whereas velocity is a vector, speed is a scalar quantity.

Simply said, velocity is the speed at which an object is moving in a particular direction. using a car travelling north on a highway as an illustration or a rocket after it has taken off as an illustration of speed. Scalar implies that the absolute magnitude of the velocity vector will always equal the speed of the motion.

186,282 miles per second is another way to express the speed of light. In dry air, the speed of sound is 343.2 meters per second.

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Mass of to object is 3 kg and 2 kg.

What is Gravitational force?

In mechanics, gravity, often known as gravitation, is the universal force of attraction that acts between all matter. It is by far the weakest known natural force and so has no effect on the internal properties of ordinary stuff. Due to its long reach and ubiquitous action, it influences the trajectories of bodies in the solar system and elsewhere in the universe, as well as the architecture and evolution of stars, galaxies, and the entire cosmos. The weight, or downward force of gravity, exerted by the Earth's mass on all bodies on Earth is proportional to their mass. The acceleration that freely falling objects experience is used to calculate gravity.

F =G(m1m2/r2)

m1m2 = [(1.00 X 10-8N)(20*10-2m)2]

/[6.67*10-11Nm2/kg2]

Now

m1-m2 =[(m1+m2)2-4m1m2] =[(5kg)2-4(6kg2)] =(1kg2) = 1kg 2m1 =

(m1+m2)+(m1-m2) = 5kg + 1kg =6kg

m1 = 3kg, m2 = 5kg,

and

m2 = 5kg - 3kg = 2kg

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Because the location of the outermost electron is unclear and we are unsure of its exact location, calculating the atomic radii is fairly challenging.

A chemical element is uniquely defined by its atoms, which are tiny pieces of substance.

An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.

The overlap of ions in a lattice structure makes it challenging to estimate the ionic radius.

Ionic radius typically decreases from group 1 to group 3 since the produced ions have a larger nuclear charge, more protons, and smaller ionic radius due to the electrons being drawn closer to the nucleus.

Calculating the atomic radii is fairly difficult because the location of the outermost electron is obscure and we are unaware of its precise location.

Thus, it is difficult to describe atomic radius and the ionic radius.

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We can determine the direction of the magnetic field of the current-carrying wire in the vicinity of the loop using the right-hand rule.

The right-hand rule is a common mnemonic in physics for remembering the direction of magnetic forces. A similar form of the right-hand rule, which is also called the right-hand grip rule, is used to find the direction of the magnetic field in a current-carrying wire.

The direction of the magnetic field made by a current in a wire curls around the wire in a ring. You can find the direction by curling your fingers and pointing your right thumb in the direction of the current in the wire. Your fingers will be curled in the same direction as the direction of the magnetic field around the current-carrying wire.

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Flow doesn't depends on absolute values of P1 and P2

Flow doesn't depends on absolute values of P1 and P2 but flow depends on pressure difference between top and bottom of each sides. This conclude that whenever  { P2-P4 = P1-P3 } flow will be stop.

after some time, difference in pressure across either components is

{  P​​​​​​(Top) - P​​​​(bottom) }

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The vertical acceleration of the ball at its highest altitude is 0 m/s.

It is possible for an item to have both zero acceleration and non-zero velocity because acceleration is the change in velocity. Since there is no change in velocity while an object is moving at a constant speed, it experiences no acceleration.

The bullet reaches its highest point when its vertical velocity is zero. The vertical portion of the velocity vector will now point downward. The projectile's horizontal range, which is determined by the object's beginning velocity, is referred to as the projectile's range.

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The reason for the first graph is because of the effects of deceleration and acceleration due to gravity while the arrangements of the graphs are; B> D > A> C.

When we plot a graph, the graph would always have to axes; the vertical axis and the horizontal axis. In this case, the vertical axis is the position and the horizontal axis is the time. The slope of this graph speaks of the displacement of the object.

Looking at the first graph, we can see that it can be able to show the motion of an object that went up and fell down as the speed of the object would decrease during the upward motion as it is decelerated due to gravity and comes to a halt at the maximum height before it is accelerated as it moves downwards.

From the graphs, the ranking of the displacements for the second set of graphs as; B> D > A> C. This is because there is a positive slope in B and D while the slope in A is zero and that in C is negative.

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Neither. The glass without the ice cube has some weight with the glass with the ice cube.

We hаve аn ice cube of mаss m floаting in the wаter. If it is floаting (in equilibrium), it will hаve to displаce enough wаter to support its weight. How much is thаt? It is just Volume = m/d, where m is the mаss of the ice cube, аnd d is the density of wаter.

Where the ice hаs melted, it turns into a wаter of volume. Volume = m/d exаctly the sаme volume аs it displаced before. So the аdded volume is the sаme, so the level of the wаter will not chаnge.

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Equation (8.10) provides the following form for the angular acceleration "alpha," which is proportional to the radius "rr," and the tangential acceleration "aa."

A wheel's angular acceleration is alpha = 6.0t4 - 4.0t2, where alpha is measured in radians per second squared and t is measured in seconds. The wheel has an angular position of +1.0 rad and an angular velocity of +2.0 rad/s at time t = 0.

=rα \s1: The most popular units for angular acceleration are rad/s2 and rad/s. 2 . Similar to how a + or - sign designates the direction of linear acceleration in one dimension, a + or - sign designates the direction of angular acceleration along a fixed axis.

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​

Pulleys are strong, efficient devices. They have the power to shift a force's direction, which makes it much simpler for us to move objects.

For the transmission of energy and motion, pulleys can be used alone or in conjunction. Sheaves are the name for rimmed pulleys with grooves. In a belt drive, pulleys are attached to shafts at their axes, and power is transferred between the shafts using endless belts that pass over the pulleys.

The four different types of pulleys are complex, compound, moveable, and fixed. A fixed and movable pulley make up compound pulleys.

The main benefit of using pulleys is that it requires less effort than simply lifting weights normally. To put it another way, it lessens the actual force needed to lift heavy objects. Additionally, the force's direction is altered.

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When a block slides at constant speed down a ramp while acted on by the forces.

A. True

B. False

C. False

The magnitude of dynamic friction is directly proportional to the magnitude of the normal force and the roughness between the sliding surfaces. The magnitude of static friction is directly proportional to the magnitude of the normal force and the roughness between the sliding surfaces. The normal force is not necessarily equal to gravity, but the force perpendicular to the surface on which the object is sliding.

In other words, the normal force is the force that pushes two surfaces together, and the stronger the normal force the stronger the frictional force. Another fairly common force is the frictional force. Similar to the normal force, it is caused by direct contact between surfaces. However, normal forces are always perpendicular to the surface while frictional forces are always parallel to the surface.

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The magnitude of Mars' gravitational field is 3.66 N/kg.

The approximate acceleration due to gravity experienced by the spacecraft is 3.66 m/s².

The gravitational fields of the Mars is calculated by applying the following equation;

E = F/m = GM/r²

where;

E = (6.626 x 10⁻¹¹ x 6.39 x 10²³) / (3.4 x 10⁶)²

E = 3.66 N/kg

The approximate acceleration due to gravity experienced by the spacecraft is calculated as follows;

F = mg = GmM/r²

g = GM/r²

where;

g = (6.626 x 10⁻¹¹ x 6.39 x 10²³) / (3.4 x 10⁶)²

g = 3.66 m/s²

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Electrical energy is converted into the kinetic energy of the spinning fan and the thermal energy of the heated coils within a hair dryer when the appliance is turned on.

Electrical energy is the capacity of the charged particles in an atom to start an action or move an object. The movement of electrons between atoms results in the production of electrical energy.

Every time you plug your toaster and phone charger into a wall socket, electrical energy is used to power them. Electric eels, batteries, and lightning are additional sources of this kind of power. However, electrical energy can also be converted into other types of energy, such as the thermal energy that warms your toaster and toasts your bread, or the mechanical energy that drives the acceleration of an electric car.

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Option A,C  It decrease the strength of the magnet and also decrease the number of coils in the solenoid.

A device called a solenoid is made up of a casing, a coil of wire, and a moving plunger (armature). A magnetic field develops around the coil when an electrical current is injected, drawing the plunger in. A solenoid, put more plainly, changes electrical energy into mechanical work.

Copper wire is twisted tightly in a coil that has several turns. The creation of a powerful magnetic field or flux occurs when an electrical current runs through this wire.

The coil is enclosed in a housing, which is often composed of steel or iron, which concentrates the magnetic field it produces.

The magnetic field's concentration, which provides the mechanical force needed to perform the action, draws the plunger to the stop.

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An example of a collision without physical contact is a charged particle being deflected by another charged particle as they travel by one another.

Another illustration is a gravitational slingshot, in which a light object moves around a much heavier object to accelerate. A collision does not require the objects to actually touch; for instance, an asteroid passing by the earth is seen as one since its course is altered by the gravitational pull of the planet. The conservation of momentum and energy can still be used to assess the collision. Yes, even without direct touch, an accident may still occur.

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electric force would a proton experience at the same point is .156 × 10⁻¹⁹ N/C.

Electric field :

The electric field is the amount of electric force per charge, and the electric force on a charge at a given point in space is the amount of charge multiplied by the electric field at that location.

E = F/q

where,

E = electric field

F = force

q = charge

A force experienced by an alpha particle = 0.250N

E = F/q

E =  0.250 /1.6 × 10⁻¹⁹

E = 0.156 × 10⁻¹⁹ N/C

electric force would a proton experience at the same point is .156 × 10⁻¹⁹ N/C.

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Answer:

Explanation:

 Given:

H = 3.6 m

V = 0 m/s

g = 9.8 m/s²

_________

V₀ - ?

Potential energy = m·g·H

Kinetic energy = m·V₀² / 2

Let's equate:

m·V₀² / 2 = m·g·H

V₀² / 2 = g·H

Starting speed:

V₀ = √ ( 2·g·H )

V₀ = √ (2·9.8·3.6) ≈ 8.4 m/s