Question

1. describe a situation in a basketball game when a player has a lot of kinetic energy. explain.

2.) describe a situation in a basketball game when a player has a lot of potential energy. explain.
3.) based on what you observed in the simulation, what factors affect kinetic energy?
4.) based on what you observed in the simulation, what factors affect potential energy?
5.) based on what you read in the pre - lab reading, why does the mechanical (total) energy of the skater not change over time (unless friction is turned on)?
6.) re - read the law of conservation of energy in the pre - lab section. what do you think happens to the skaters energy when friction is involved? (look back to questions 11 and 12.)
7.) an archer stands on the ground and fires an arrow at a target. a second archer stands at the top of a building and holds an arrow in his hand. which arrow has more potential energy? explain.
8.) in the same scenario described in question 7, which arrow has more kinetic energy? explain.

Explanation:

Step1: Define kinetic energy

Kinetic energy ($KE$) is given by $KE=\frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity. A basketball - player has a lot of kinetic energy when running fast to make a fast - break. For example, a player dribbling the ball at high speed down the court has a large velocity, and assuming a non - zero mass, the formula $KE = \frac{1}{2}mv^{2}$ shows that a high velocity leads to a large kinetic energy.

Step2: Define potential energy

Gravitational potential energy ($PE$) is given by $PE = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height. In a basketball game, a player has a lot of potential energy when they are high in the air, such as when jumping to make a dunk. At the maximum height of the jump, the player has a non - zero height $h$ above the ground, and with mass $m$ and the acceleration due to gravity $g$, the formula $PE=mgh$ indicates a large potential energy.

Step3: Identify factors affecting kinetic energy

From the formula $KE=\frac{1}{2}mv^{2}$, the factors affecting kinetic energy are mass ($m$) and velocity ($v$). An increase in either the mass or the velocity of an object will increase its kinetic energy. For example, a heavier player running at the same speed as a lighter player will have more kinetic energy, and a player increasing their running speed will increase their kinetic energy.

Step4: Identify factors affecting potential energy

From the formula $PE = mgh$, the factors affecting gravitational potential energy are mass ($m$), the acceleration due to gravity ($g$), and height ($h$). On Earth, $g$ is approximately constant. So, an increase in mass or height will increase the potential energy. For example, a taller player jumping to the same height as a shorter player will have more potential energy due to their greater mass, and a player jumping higher will have more potential energy.

Step5: Explain conservation of mechanical energy

In the absence of non - conservative forces like friction, the mechanical energy ($E = KE+PE$) of the skater is conserved. This is because energy can only be converted between kinetic and potential forms. For example, as the skater moves down a ramp, potential energy is converted into kinetic energy, and as the skater moves up a ramp, kinetic energy is converted into potential energy, but the sum $KE + PE$ remains the same.

Step6: Analyze energy with friction

When friction is involved, the mechanical energy of the skater is not conserved. Friction is a non - conservative force that dissipates energy as heat. As the skater moves on a surface with friction, some of the mechanical energy is converted into heat energy, causing the skater's total mechanical energy ($KE + PE$) to decrease over time.

Step7: Compare potential energy of arrows

The second archer's arrow (the one held by the archer at the top of the building) has more potential energy. Using the formula $PE=mgh$, assuming the mass of the arrows is the same and $g$ is constant, the arrow at a higher height ($h$) (the one at the top of the building) has more potential energy.

Step8: Compare kinetic energy of arrows

The first archer's arrow (the one that is fired) has more kinetic energy. The arrow fired by the archer on the ground has a non - zero velocity ($v$), and using the formula $KE=\frac{1}{2}mv^{2}$, while the arrow held by the archer on the top of the building has zero velocity (initially) and thus zero kinetic energy (assuming it is not yet released).

Answer:

1. A player running fast to make a fast - break has a lot of kinetic energy because kinetic energy $KE=\frac{1}{2}mv^{2}$ and a high velocity $v$ leads to a large $KE$.
2. A player jumping to make a dunk has a lot of potential energy because at the maximum height of the jump, with $PE = mgh$, a non - zero height $h$ gives a large $PE$.
3. Mass and velocity affect kinetic energy. An increase in either will increase kinetic energy.
4. Mass and height affect potential energy (on Earth, $g$ is constant). An increase in either will increase potential energy.
5. In the absence of non - conservative forces like friction, energy is only converted between kinetic and potential forms, so the mechanical energy ($KE + PE$) is conserved.
6. Friction is a non - conservative force that dissipates energy as heat, so the skater's mechanical energy decreases over time.
7. The arrow held by the archer at the top of the building has more potential energy because $PE=mgh$ and it has a greater height $h$.
8. The arrow fired by the archer on the ground has more kinetic energy because it has a non - zero velocity $v$ and $KE=\frac{1}{2}mv^{2}$, while the arrow held by the archer on the top of the building has zero velocity (initially).