Electrolytic cells require an input of energy, and are used to plate metals by functionally running a voltaic cell in reverse.

For electrolytic cells, the cell potential is negative; in contrast, galvanic/voltaic cells have positive cell potentials. Electrolysis reactions can only occur if the total potential is positive. An additional voltage input, such as a battery, is required so that the sum of potentials in the electrolytic cell is greater than zero.

Oxidation always occurs at the anode, regardless of cell type, and electrons always travel toward the site of reduction (the cathode). In a galvanic cell, the cathode is positively charged, naturally drawing the flow of electrons. In an electrolytic cell, the cathode is negatively charged, but still requires the flow of electrons to allow reduction to occur. An induced current from a battery is used to propel these electrons against their natural flow.

Electrolysis is a specific type of reaction that occurs in an electrolytic cell. An electrochemical cell contains an anode and a cathode that facilitate a redox reaction. In an electrolytic cell (a type of electrochemical cell) the redox reaction that is carried out is a nonspontaneous reaction. Recall that the change in Gibbs free energy for a nonspontaneous, or unfavorable, reaction is always positive; therefore, for electrolysis in an electrolytic cell, the redox reaction has a . Statement I is false.

Nonspontaneous reactions are reactions that are unfavorable. This means that energy is required to carry out the reaction. In an electrolytic cell, energy is provided in the form of voltage input. The voltage provided pushes the reaction in the unfavorable direction; therefore, electrolysis reactions require a voltage source. Statement II is true.

Since it requires energy, an electrolysis reaction is considered to be an endothermic process. Recall that endothermic processes are reactions that take in (or require) energy, whereas exothermic processes are reactions that release energy; therefore, electrolysis is an endothermic process. Statement III is false.

The question states that the reaction has a negative ; therefore, the reaction is nonspontaneous. Nonspontaneous reactions are carried out in electrolytic cells (as opposed to galvanic cells). A reaction usually proceeds in the spontaneous direction; therefore, to carry out nonspontaneous reactions you must put energy into the system. Without energy, the reaction shown will occur in the reverse direction.

In an electrolytic cell, energy is provided by an external voltage source. Without energy, the electrolytic cell will have a voltage of  and the spontaneous (reverse) reaction will occur. For the nonspontaneous reaction to occur, you must attach a voltage source in such a way that the voltage applied is greater than  and is applied in the opposite direction (nonspontaneous reaction direction). This will force the reaction in the reverse direction and the nonspontaneous reaction will occur; therefore, the external voltage source must provide a voltage greater than .

Use conservation of momentum in each direction:  and 

The initial momentum in the x direction is provided only by the first object.

This also equals the final x-momentum, when the two objects move together at the same velocity.

The initial momentum in the y direction is provided only by the second object.

Again, this equals the final y-momentum.

Combine the two velocities using the Pythagorean theorem.

The momentum is equal to Sam's total mass times his velocity. His velocity can be found from his potential energy, using conservation of energy. Keep in mind, his total mass includes the mass of his sled.

PE = mgh = (50kg + 10kg) * 10m/s² * 50m

PE = 30,000J

KE = 30,000J = 1/2mv² = 1/2(60kg)(v²)

v² = 1000 m²/s² = 31.2m/s

p = mv = 60 kg * 31.2 m/s = 1898 kg*m/s

If you had used 30J in place of 30kJ in the KE calculation, you would have chosen 60kg*m/s

Kinetic energy emphasizes velocity, by squaring the velocity term.

KE = 1/2mv²

Sally's KE = 1/2(52 kg)(12 m/s)² = 3,744J

John's KE = 1/2(80 kg)(8m/s)² = 2,560J

p = mv

Sally's Momentum = 52kg * 12m/s = 624 kg*m/s

John's Momentum = 80kg * 8m/s = 640 kg*m/s

Apply conservation of momentum before and after the collision.

.

Taking left to be the negative direction, and noting that Bob's initial momentum is 0 since he is at rest, we can use the provided information to see that  .

Solving for , we get . Since this answer is positive, Bob's momentum is in the positive direction (to the right).

The difference between an elastic and inelastic collision is that in an elastic collision BOTH momentum and kinetic energy are conserved. Momentum is conserved in any collision, but when a collision is inelastic, kinetic energy is dissipated when the two individual objects combine. This energy can be in the form of heat, explosion, sound, etc. In a totally inelastic collision, the two objects colliding stick together and travel with the same velocity in one direction.

Overall energy is conserved, as the energy is merely transferred from a kinetic form to a non-kinetic form.

We can find the momentum for each object using the momentum formula, .