### For an electrostatic precipitator, the radius of the central wire is 90.0 um, the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kV is established between the wire and the cylinder. What is the magnitude of the electric field midway between the wire and the cylinder wall?

The aim of this question is to understand the basic working principle of the electrostatic precipitator by applying the key concepts of static electricity including electric field, electric potential, electrostatic force, etc. Electrostatic precipitators are used to remove undesired particles (especially pollutants) from smoke or effluent gases. They are used mostly in coal-powered power plants […]

### How many electrons per second enter the positive end of battery #2 for the following circuit:

This circuit is made up of two wires and two batteries. All components are connected in series such that the positive terminal of battery # 2 is electrically connected to the negative terminal of battery # 1. A steady current flows through this circuit. Each battery has an emf of $1.3$ volts Each […]

### A piston–cylinder device initially contains 0.07 cubic meter of nitrogen gas at 130 kPa and 180 degrees. The nitrogen is now expanded to a pressure of 80 kPa polytropically with a polytropic exponent whose value is equal to the specific heat ratio (called isentropic expansion). Determine the final temperature and the boundary work done during this process.

This problem aims to familiarize us with different state laws of physics and chemistry involving temperature, volume, and pressure. The concepts required to solve this problem include Boyle’s law, the ideal gas law, and work done using polytropic processes. First, we will look at Boyle’s law, which is a practical gas law that defines how the […]

### Nitrogen is compressed by an adiabatic compressor from 100 kPa and 25°C to 600 kPa and 290°C. Calculate the entropy generation for this process, in kJ/kg∙K.

The aim of this problem is to find the entropy generation value of an adiabatic process in which nitrogen is compressed at a given temperature and pressure. The concept required to solve this problem is related to thermodynamics, which includes the entropy generation formula. In general terms, entropy is described as a standard of randomness […]

### Viewed from a point above the north pole, is the angular velocity positive or negative?

– The radius of the earth is measured to be $6.37times{10}^6m$. It completes one rotation around its orbit in $24$ hours. – Part (a) – Calculate the angular speed of the earth. – Part (b) – If the rotation of the earth is viewed from a location above the north pole, will the angular velocity […]

### What is the smallest value the angle θ can have with a rope without breaking it.

This question aims to find the value of the smallest angle theta can make with a rope without breaking it by using laws of motion. Consider a box of sweets weighing down the rope when people from across the buildings are sending this box. People from one building are sending this box of sweets to […]

### A rubber ball of mass m is dropped from a cliff. As the ball falls. it is subject to air drag (a resistive force caused by the air). The drag force on the ball has magnitude bv^2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.

(a) Write but do not solve the differential equation for the instantaneous velocity $v$ of the ball in terms of time, given quantities, quantities, and fundamental constants. (b) Determine the final velocity $vt$ intervals of the given quantities and basic constants. The article aims to find the differential equation of instantaneous velocity and terminal velocity. This article uses the […]

### A clay vase on a potter’s wheel experiences an angular acceleration of 5.69 rad/s^2 due to the application of a 16.0 nm net torque. find the total moment of inertia of the vase and potter’s wheel.

This article aims to find the moment of inertia in the given system. The article uses the concept of Newton’s second law for rotational motion. -Newton’s second law for rotation, $sum _ { i } tau _ { i }= I alpha$, says that the sum of torques on a rotating system about a […]

### If you double the net force on an object, you’ll double its

– Acceleration. – Velocity. – Speed. – All of the above. Choose the correct option from the given choices. The main objective of this question is to choose the correct option from the given options when you apply double force on an object. This question uses the concept of Newton’s second law of motion. Newton’s […]

### The three balls each weigh 0.5 lb and have a coefficient of restitution of e = 0.85. If ball A is released from rest and strikes ball B and then ball B strikes ball C, determine the velocity of each ball after the second collision has occurred. The balls slide without friction.

The aim of this question is to find the change in speed of two bodies after collision by utilizing the concept of elastic collisions. Whenever two bodies collide, their momentum and energy remain constant as per the energy and momentum conservation laws. Based on these laws we derive the concept of elastic collisions where the […]

### A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37 degrees with the horizontal.

Determine the following quantities: – The horizontal and vertical components of the velocity vector. – The maximum height reached by the projectile above the launch point. The aim of this question is to understand the different parameters during 2D projectile motion. The most important parameters during the flight of a projectile are its range, time […]

### For how long a time t could a student jog before irreversible body damage occurs?

– Thermal energy is generated at a rate of $1200W$ when a student weighing $70-kg$ is running. – This thermal energy must be dissipated from the body through perspiration or other processes to maintain the body temperature of the runner at a constant $37 ^{ circ }C$. In the event of failure of any such […]

### The figure shows a laser beam coming from the left, deflected by a 30-60-90 prism. What is the prism’s index of refraction?

This problem aims to find the refractive index of a prism having angles of $30space60$ and $90$ degrees. The concepts required to solve this problem are related to snell’s law and the index of refraction. Now the refractive index is defined as the ratio of the speed of light in any medium (e.g. water), to […]

### The wave speed on a string under tension is 200 m/s. What is the speed if he tension is doubled?

The aim of this question is to understand the key concepts of speed, frequency, wavelength, and tension in a string. Whenever energy is transferred from one place to another through the successive vibratory motion of particles, this form of energy transferring agent is called a wave. All type of waves have some common properties such […]

### A bicycle with 0.80 m diameter.

This question aims to find the angular speed of the tires of the bicycle and the speed of the blue dot painted on the tires of 0.8m diameter. A bicycle is coasting on a level road at a speed of 5.6 m/s. The tires of this bicycle have a diameter of 0.80 m and a […]

### What is a Frequency distribution of qualitative data and why is it useful?

This question aims to find the frequency distribution of the qualitative data by using knowledge of the frequency distribution. Frequency distribution is a representation of several observations in a tabular form. It displays information within the given intervals. A frequency distribution shows the number of repeated items in a tabular or descriptive form. It can be […]

### Rachel has good Distant vision but has a touch of Presbyopia. Her near point is $0.80$ m.

This question aims to find the near point and far point of Rachel when she wears +2.0 D reading glasses. Rachel has a good distant vision but she has a touch of presbyopia. Her near point is 0.60 m. The maximum distance at which the eyes can see things properly is called the far point […]

### The components of a velocity field are given by u= x+y, v=xy^3 +16, and w=0. Determine the location of any stagnation points (V=0) in the flow field.

This question belongs to the physics domain and aims to explain the concepts of velocity, velocity field, and flow field. Velocity can be described as the rate of transformation of the object’s position concerning a frame of concern and time. It sounds complex but velocity is essentially speeding in a particular direction. Velocity is a […]

### What is the angle between the electric field and the axis of the filter?

This question aims to find the angle between the electric field and the axis of a filter when a polarized light wave passes through the polarizing filter. The property of the electromagnetic radiation passing through a polarizing filter in a certain direction having a magnitude of vibrating electric field is called polarization. The light waves […]

### Find a2, the magnitude of the centripetal acceleration of the star with mass m2 under the following constraints.

There is a binary star system comprising of a pair of stars with masses denoted by $m_1$ and $m_2$ and centripetal acceleration denoted by $a_1$ and $a_2$. Both the stars, while attracting each other, circulate around a center of rotation of the combined system. This question aims […]

### Boxes A and B are in contact on a horizontal, frictionless surface. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

The aim of this question is to understand and apply Newton’s laws of motion to moving objects. According to Newton’s motion laws, a body can’t just move by itself. Instead, an agent called the force acts on a body to move it from rest or to stop it. This force causes the change in speed, […]

### Two light bulbs have constant resistances of 400 ohm and 800 ohm. If the two light bulbs are connected in series across a 120 V line, find the power dissipated in each bulb

The main objective of this question is to find the power dissipated in each bulb that is connected in series. This question uses the concept of power in series. In a series circuit, the total power is the same as the total amount of power lost by each resistor. Mathematically, it is represented as: [ […]

### Find the scalar and vector projections of b onto a.

– $space a space = space (4, space 7, space -4), space b space = space (3, space -1, space 1)$ The main objective of this question is to find the scalar and vector of one vector onto the other vector. This question uses the concept of vector and scalar projection. A vector […]

### At a certain location wind is blowing steadily at 12 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60m diameter blades at that location. Take the air density to be 1.25kg/m^3.

This question aims to develop an understanding of the power generation capacity of a wind turbine generator. A wind turbine is a mechanical device that converts the mechanical energy (kinetic energy to be precise) of the wind into electrical energy. The energy generation potential of a wind turbine depends upon the energy per unit mass […]

### A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 24 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 175m) the block swings toward the outside of the curve, then the string makes an angle theta with the vertical. Find theta.

This question aims to develop a practical understanding of Newton’s laws of motion. It uses the concepts of tension in a string, the weight of a body, and the centripetal/centrifugal force. Any force acting along a string is called the tension in the string. It is denoted by T. The weight of a body with […]

### How far, in meters, will the vehicles slide after the collision?

A car with mass mc=1074kg is traveling west through an intersection at a magnitude of veloctiy of vc=15m/s when a truck of mass mt=1593 kg traveling south at vt=10.8 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficiet of friction of […]

### Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted?

The main objective of this question is to find the wavelength of light which is related to the electron transition when it jumps from lower energy state to higher level of energy.This question uses the concept of the wavelength of light. The distance between the two subsequent crests or troughs is known as the light […]

### Calculate the total kinetic energy, in Btu, of an object with a mass of 10 lbm when its velocity is 50 ft/s.

The aim of this article is to find the Kinetic Energy of an object in motion in $BTU$. The basic concept behind this article is the understanding of Kinetic Energy K.E. and its unit conversion. Kinetic Energy is defined as the energy that an object carries while in motion. All moving objects possess kinetic energy. […]

### A point charge of magnitude q is at the center of a cube with sides of length L. What is the electric flux Φ through each of the six faces of the cube? What would be the flux Φ_1 through a face of the cube if its sides were of length L_{1}?

This article aims to find the electric flux in a cube having six sides. This article uses the concept of electric flux. For a closed gaussian surface electric flux is given by the formula [Phi_{e} = dfrac{Q}{xi_{o}}] Expert Answer Consider a cube having side length $L$ in which a size $q$ charge is placed at […]

### An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R.

Write an expression from the given data to calculate the mass of the planet concerning G and the variables given in the statement. Also calculate the mass of the planet in Kg if T=26 hours and R=2.1X10^8m. This problem aims to familiarize us with the objects revolving around a specific pivot point. The concepts required to solve this problem are mostly […]

### A 0.500-kg mass on a spring has velocity as a function of time given by the following equation. Find the following:

[ v_x(t) = ( 2.60 cm/s) sin big[ ( 4.63 rad/s ) t – (pi/2) big] ] The Period The Amplitude Maximum Acceleration of the Mass Force Constant of the Spring The question aims to find the period, amplitude, acceleration, and force constant of the spring of a mass attached to a spring. The question […]

### A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. Calculate the speed and frequency of light in given solid.

This question aims to study the effect of material on the wave speed when it travels from one material to another. Whenever a wave strikes the surface of another material, a part of it is bounced back into the previous medium (called reflection phenomenon) and a part of it enters into the new medium (called […]

### How much work is done on the package by friction as it slides down the circular arc from A to B?

– A railway station has a loading yard for goods transport, a small 0.2kg documents package is released from rest to a point A on a booking place which is one-quarter of a circle having the radius of 1.6 m. The package size is much smaller compared to a radius of 1.6 m. Therefore, the […]

### Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position.

a(t)= 2i+2kt, v(0)=3i-j, r(0)=j+k This question aims to find a particle’s velocity and position vector with some acceleration, initial velocity, and position vectors. A position vector helps us find one object’s position relative to another. Position vectors normally start at the origin and […]

### A parallel-plate air capacitor has a capacitance of 920 pf. The charge on each plate is 3.90 μc.

Calculate the potential difference existing between the plates of the capacitor. Keeping the charge constant on each plate of the capacitor, calculate the impact of doubling the separation between capacitor plates on the potential difference. Calculate the amount of work that will be required to double the separation between the capacitor plates. The aim of […]

### Two small spheres spaced 20.0 centimeters apart have equal charges.

If the spheres repel each other with a repulsive force having a magnitude of 3.33X10^(-21) N, calculate the excess electrons that each sphere carries. This question aims to find the number of excess electrons present on a set of bodies that causes them to repel each other. The basic concept behind this article is the […]

### Determine the current (magnitude and direction) in the 8.0 and 2.0-? resistors in the drawing.

This problem aims to familiarize us with different circuital laws and circuit analysis. The concepts required to solve this problem are related to Kirchoff’s circuit laws, which include Kirchoff’s first law, known as the current law, and Kirchoff’s second law, known as the voltage law. In circuit analysis, Kirchhoff’s circuit laws help to form an […]

### A movie stuntman (mass 80.0kg) stands on a window ledge 5.0m above the floor. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie’s villian (mass 70.0 kg), who is standing directly under the chandelier.(assume that the stuntman’s center of mass moves downward 5.0 m. He releases the rope just as he reaches the villian. (a) with what speed do the entwined foes start to slide across the floor?

If the coefficient of kinetic friction of their bodies with the floor is 0.250, how far do they slide? The question aims to understand newton’s law of motion, the law of conservation, and the equations of kinematics. Newton’s law of motion states that the acceleration of any object relies on two variables, the mass of […]

### What is the width of the central bright fringe?

A light beam whose wavelength $lambda$ is 550nm is passing through a single slit having a width of the slits equals to 0.4mm and hits a screen that is placed 2m away from the slit. This question aims to find the width of the central bright fringe of the light that is passing through a […]

### What is the acceleration of the block when x= 0.160 m?

This question aims to find the acceleration of the block attached to a spring that is moving along a frictionless horizontal surface. This block follows the simple harmonic motion along the horizontal direction. Simple harmonic motion is the type of “to and fro” motion in which the object displaced from its mean position by an acting […]

### Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.

The main objective of this question is to resolve the given vector into its component and determine its magnitude. This question uses the concept of Vector resolution. A vector resolution is the breaking of such a single vector into several vectors in various directions that collectively generate the same effect as a single vector. Component […]

### What is the block’s speed now?

This question aims to find the speed of the block when it gets released from its compressed state. The spring of the block is compressed by length delta x from its initial length $x_o$. The tension and compression present in the spring obey Hooke’s law which states that the minor displacements in the object are […]

### A high diver of mass 70.0 kg jumps off a board 10 m above the water. If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

The aim of this question is the application of the energy conservation law (kinetic energy and potential energy). From the definition of the energy conservation law, any form of energy can neither be destroyed nor created. However, energy may be interconverted between its different forms. The kinetic energy of a body denotes the energy it possesses […]

### On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m/s due to a friction force that is 25% of her weight. Use the work–energy theorem to find the length of this rough patch.

This problem aims to find the length of a rough patch using the concept of the work-energy theorem and the Principle of Energy Conservation. It also covers the study of the non-conservative force of friction between ice and skates. The most important concept discussed here is the work-energy theorem, most commonly known as the principle of […]

### What is the electric flux through a spherical surface just inside the inner surface of the sphere?

– A conducting sphere with a hollow cavity inside has an outer radius of $0.250m$ and an internal radius of $0.200m$. A uniform charge exists on its surface having a density of $+6.37times{10}^{-6}dfrac{C}{m^2}$. Inside the cavity of the sphere, a new charge having a magnitude of $-0.500mu C$ is introduced. – (a) Calculate the new […]

### The asteroid belt circles the sun between the orbits of Mars and Jupiter.

The period of the asteroid is assumed to be $5$ Earth Years. Calculate the speed of the asteroid and the radius of its orbit. The aim of this article is to find the speed at which the asteroid is moving and the radius of its orbital movement. The basic concept behind this article is Kepler’s […]

### A boat on the ocean is 4 miles from the nearest point on a straight shoreline; that point is 6 miles from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant.

If she walks at $3, mi/hr$ and rows at $2, mi/hr$, at which point on the shore should she land to minimize the total travel time? If she walks at $3, mi/hr$, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with […]

### A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible.

what is the speed of the rock when the string passes through the vertical position? what is the tension in the string when it makes an angle of $45$ with the vertical? what is the tension in the string as it passes through the vertical? The purpose of this question is to find the speed […]

### The electric potential at a point that is halfway between two identical charged particles is 300 V. What is the potential at a point that is 25% of the way from one particle to the other?

The idea of this question is to find the electric potential between two charges given some conditions. The electric potential is regarded as the small amount of energy required for one unit of charge for a test charge such that the disruption of the field taken can be neglected. Its magnitude is determined by the amount […]

### The deepest point in the ocean is 11 km below sea level, deeper than MT. Everest is tall. What is the pressure in atmospheres at this depth?

This question aims to find the atmospheric pressure given the depth of a point. The pressure of the atmosphere on the surface is defined as atmospheric pressure. It is measured in atm (atmosphere), whereas at the sea level, the average pressure is taken to be $1$ atm. It is also known as barometric pressure or […]