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Science
1) There might be various possible answers to this question. One way to return to your spaceship is by throwing the wrench in the direction opposite to the direction between your and the ship. This...
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Iraq is rich in oil and natural gas deposits, so there has been minimal motivation on the part of the Iraqi government to pursue alternative sources of energy. Ideally, it would develop renewable...
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Equinoxes and solstices happen due to the tilt of the Earth on its axis. Solstices occur when the Earth is at a maximum angle away from the Sun. During the summer solstice the sun is directly...
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1). Coordinate covalent bond: This is a type of covalent bond in which two atoms are sharing a pair of electrons, but both the electrons are coming from the same atom. This is as opposed to a...
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Science
The force diagram below shows the forces acting on the sphere and the hanging object. The tension in the string is responsible for the angular acceleration of the sphere and the difference between...
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There are two quantities which effect the reading on the scale. The weight of the chain that has accumulated on the scale after falling a distance x and the impulse per unit time imparted by the...
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Use the definition of reactance to find the reactance of the inductor at any frequency. Then plug in the values and evaluate.
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Successive peaks are one-half period apart. See attached image below.
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I= qnAv relates the current I in a wire to the charge q of the charge carriers, the number density n of charge carriers, the cross-sectional area A of the wire, and the drift velocity v of the...
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Use Gauss's law relate the electric flux with the charge enclosed in the box. Since the electric flux is directly proportional to the net amount of enclosed charge in the box, if the flux is zero,...
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Lets say point P is a distance z above the central axis of the disk. We will integrate concentric rings of charge, with thickness dr, from the center of the disk to the edge. From symmetry, all...
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First, use the definition of λ to find the total charge of the line of charge. Integrate the line of change along the axis to find electric field. The line of charge is positive, and since the...
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Use the definition of rotational kinetic energy. First, to find Earths rotational KE use it when I is its moment of inertia with respect to Earth's axis of rotation. Next to find the orbital know...
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The diagram below shows the forces acting on both objects and the pulley. The direction of motion has been chosen to be the +x direction. By applying Newton’s second law of motion, obtain a...
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Since the blocks are in equilibrium, use Newton's second law to sum all the components of the gravitational forces that lie along the rope and set them equal to zero. The tension forces are all...
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To escape the gravity of the moon the kinetic energy an object must have must be equal to or greater than the gravitational potential energy of the moon. So set the kinetic and gravitational...
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Use the law of gravity to find the gravitational force acting on the satellite. The application of Newton’s second law will lead us to the speed of the satellite and its period can be found from...
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You could apply Newton’s law of gravitation and second law of motion to solve this problem from first principles, but I will use Kepler’s third law (which is derived from these laws) to find...
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The moment of inertia of a system of particles with respect to a given axis is the sum of the products of the mass of each particle and the square of its distance from the given axis.
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The key to this problem is knowing that the Earth rotates through 2π radians every 24 hours. Then apply the definitions of angular speed.
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The impulse delivered to the ball equals the change in the ball’s momentum. The impulse is also the product of the average force exerted on the ball and the time during which the average force...
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The net external force on the objects is zero and linear momentum is conserved as the spring delivers its energy to the two objects. Choose a coordinate system in which the +x direction is to the...
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Solve for V by knowing that the difference in potential energy is the dot product of the electric field and the infinitesimal path length integrated over the entire path of the particle (from `b`...
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Assume, for these electrons, their motion is from left to right through the velocity selector and the electric field is upward. This means the electric force is downward and hence then the magnetic...
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First, apply Newton’s second law to the orbiting proton to relate its speed to its radius. After, use the definition of its period (T) to eliminate r and calculate a value for T. Then find the...
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The net electric force on q0 is the vector sum of the individual electric forces exerted on q0. Compute each force from Coulomb's law and write it in terms of its rectangular components. Then use...
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Use Coulomb's law to determine the magnitude of the electrostatic force of attraction exerted by the proton on the electron. The magnitude of both the electron and proton charge is equal to the...
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Model this circumstance as a rope of negligible mass with one end attached to the limb and the other end attached to a particle of mass m. Apply Newton's second law to the mass. Solve for the...
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We can find `B` from the generalized form of Ampere's law. Choose a circular path of radius `r=2.0 cm` about the center line joining the two plates, as shown in the diagram below. Ampere's law...
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Since the wind is blowing to the east, a plane headed due north will drift off coarse toward the east.Hence, to compensate for this crosswind, the plane must head west of due north. We must use...
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We can use the definition of entropy change to find the change in entropy of the liquid water as it freezes. The change of entropy of the water is given by: `DeltaS=Q_(rem)/T` Where the heat...
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The efficiency of a heat engine is the ratio of work done per cycle `W` to the heat absorbed from the high temperature reservoir `Q_h` . The efficiency epsilon is therefore: `epsilon=W/Q_h` The...
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We can express the rms speed of Argon atoms by combining the ideal gas law with the equation for the root mean square velocity of an atom. The ideal gas law is: `PV=nRT` The rms velocity of a...
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There are two main forms of nuclear energy, fission, which involves splitting atoms apart, and fusion, which involves releasing energy when 2 atomic nuclei are forced close together and fuse into a...
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The de Broglie relation is `eq. (1) ->` `P=h/lambda` Now get the momentum `P` in terms of the kinetic energy `K_E` . `K_E=1/2 mv^2` `K_E=P^2/(2m)` `eq. (2) ->` `P=sqrt(2mK_E)` Therefore the...
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The change in the wavelength, `Delta lambda` , is given by the famous Compton formula. `Delta lambda = h/(m_e c)(1-cos(theta))` Now plug in the values for the electrons mass `m_e` , the speed of...
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The work function of a metal `phi` , the wavelength of the incident photon lambda required to eject an electron with the maximum kinetic energy `K_(max)` is expressed by Einsteins photoelectric...
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This can be solved by applying Poiseuille's law. `Delta P=(8 eta L)/(pi r^4)*I_v` where: `eta` = viscosity `L` = length of the pipe `r` = radius of the pipe `I_v` = volume flow rate Therefore...
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The pressure applied to an enclosed liquid is transmitted undiminished to every point in the fluid and to the walls of the container. Hence we can equate the pressure produced by the force applied...
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The question states that 1 atmosphere of pressure, 101,000 Pa, is already present. In order to achieve 2 atmospheres of pressure, we need increase our pressure by another 101,000 Pa. That can be...
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We can use the continuity equation to compare the flow rates at the two locations. `A_A*v_A=A_B*v_B` This equation relates the area and velocity of pipe `A` to that of `B` . Solve for `v_A` ....
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The water level in the pond will fall slightly. When the anchor is in the boat, the boat displaces enough water so that the buoyant force on it equals the sum of the weight of the boat, your...
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The attached diagram shows the displacement of the pendulum bob, through an angle theta, as a consequence of the complete absorption of the incident radiation. Now use conservation of mechanical...
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We can use the definition of pressure to express the radiation force on the balloon. We'll assume that the gravitational force on the balloon is approximately its weight at the surface of Earth,...
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The minimum possible force to move the block has to be just equal to the maximum possible value of static friction. (Static friction is the friction force between the table and the block that keeps...
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The speed of the second block v can be found from the equation of motion involving the distance and acceleration: `v^2 - v_i^2 = 2ad` Assuming the second block is falling from rest, that is, `v_i =...
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In general, the contribution to the total electric field `E` from an infinitesimal piece of charge `dE` is `dE=(k*dq)/r^2` The total field is then calculated by integrating over all the charge:...
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The Bohr formula gives `E=E_0/n^2` for the nth excited state with `E_0=13.6 eV` being the ground state energy. The relationship between energy and wavelength is `Delta E=hc/(Delta lambda)` `Delta...
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We are going to use conservation of angular momentum for this problem. We are going to need the moment of inertia for a rod rotating about its end. I will derive it here using the formula for the...
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Remember the definition of the commutation relation `[a,b]=ab-ba` Preform this operation on `[S_x*S_y,S_y]` `[[S_x*S_y,S_y],S_z]=[[S_x*S_y*S_y-S_y*S_x*S_y,S_z]` The following is the commutation...