
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...

Science
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...

Science
Use the definition of reactance to find the reactance of the inductor at any frequency. Then plug in the values and evaluate.

Science
Successive peaks are onehalf period apart. See attached image below.

Science
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 crosssectional area A of the wire, and the drift velocity v of the...

Science
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,...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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.

Science
The key to this problem is knowing that the Earth rotates through 2π radians every 24 hours. Then apply the definitions of angular speed.

Science
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...

Science
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...

Science
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`...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
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...

Science
The change in the wavelength, `Delta lambda` , is given by the famous Compton formula. `Delta lambda = h/(m_e c)(1cos(theta))` Now plug in the values for the electrons mass `m_e` , the speed of...

Science
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...

Science
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...

Science
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...

Science
The pressure due to a column of height `h` of a liquid of density `rho` is given by its weight per unit area. The pressure as a function of height is then: `P(h)=W/A=(mg)/A=((rhoV)g)/A=rho g h `...

Science
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` ....

Science
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...

Science
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...

Science
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,...

Science
The static force opposes the motion of the object, and the maximum value of the staticfriction force is proportional to the normal force `F_n` . The normal force is equal to the vertical...

Science
First lets set up our coordinate system. Let the xaxis follow the string and have it be +x up the ramp for block 1 and +x for block 2 be downward. We will then have the yaxes for block 1 be...

Science
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:...

Science
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...

Science
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...

Science
Remember the definition of the commutation relation `[a,b]=abba` Preform this operation on `[S_x*S_y,S_y]` `[[S_x*S_y,S_y],S_z]=[[S_x*S_y*S_yS_y*S_x*S_y,S_z]` The following is the commutation...

Science
The speed of a point on the disk at a distance `r'` for `0lt= r' lt=r` from the axis is `v=omega r'` , so the force per unit charge is `f_(mag)=v xx B=omega r' B` radially outward. The emf is...

Science
Use the Lorentz force on a charge `Q` , when `Q` moves an amount `dl` . Then we also know that work is the dot product of force and distance. `dW_(mag)=F_(mag)*dl=Q(v xx B)*dl` But `dl=v dt`...

Science
For a continuous potential to equation is `V=int (k*dq)/r` Where `k=1/(4pi epsilon_0)` , `dq` is an infinitesimal piece of charge, and `r` is the distance away `dq` is from the point we are...

Science
First use conservation of energy to find `v` at the bottom of the ramp when there is no friction. `E_i=E_f` `mgh=1/2mv^2` `v=sqrt(2gh)` Now plug into a kinematic equations to find `t` after the...