Use the spreadsheet below to answer the question. A student uses a spreadsheet application to create a computational model of energy changes experienced by an object in free fall. Which formula could the student have entered into cell E2 of the spreadsheet? (1 point) Responses =$B$3*9.8*D2 =$B$3*9.8*D2 =$B$2-9.8*C2 =$B$2-9.8*C2 =0.5*9.8*C2^2 =0.5*9.8*C2^2 =0.5*$B$3*E2^2
The question seems to involve a spreadsheet with columns that relate to an object in free fall, but the actual data and specific content of each column (A, B, C, D, and E) has not been provided. However, I can attempt to deduce the formula that might be relevant to a commonly modeled aspect of free fall: gravitational potential energy (PE), kinetic energy (KE), or total mechanical energy (if we are assuming there's no air resistance).
In the context of free fall:
1. Potential Energy (PE) at a height h is given by PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s²), and h is height.
2. Kinetic Energy (KE) of an object with mass m moving at velocity v is given by KE = 0.5 * m * v².
3. Total mechanical energy in the absence of air resistance remains constant and is the sum of PE and KE.
Given the formulas you've listed, we can make some educated guesses about what each one represents and which might be suitable for cell E2, depending on what the student is calculating:
- =$B$3*9.8*D2: This could represent the gravitational force (weight) on the object (mass * acceleration due to gravity * some other factor), but without knowing the content of cell D2, it’s hard to determine if this is correct.
- =$B$2-9.8*C2: This isn't a standard equation used in free fall calculations, it subtracts a product of gravity and the value in C2 from the value in B2, so its relevance depends on what those cells represent.
- =0.5*9.8*C2^2: This looks like a variation of the kinetic energy formula but incorrectly substitutes the acceleration of gravity for mass (it should be 0.5 * m * v², not 0.5 * g * v²).
- =0.5*$B$3*E2^2: This appears to be a kinetic energy formula assuming that B3 contains mass (m) and E2 contains velocity (v). It could be correct if E2 is expected to hold a velocity value and B3 is mass.
If E2 is intended to calculate the gravitational potential energy of an object at height h, using the known value of g and mass from B3, the correct formula would look like this:
=E2 = $B$3 * 9.8 * D2 (assumes that D2 contains the height h)
If E2 is intended to calculate the kinetic energy of an object falling from height h, the correct formula would look something like this (assuming velocity v is in some cell, say F2):
=E2 = 0.5 * $B$3 * F2^2
Without knowing the specifics of the spreadsheet, however, I can't give a definitive answer as to which formula is correct. The student should identify what each cell represents and choose a formula that correctly applies to the physical quantity being calculated.
Use the spreadsheet below to answer the question. A student uses a spreadsheet application to create a computational model of energy changes experienced by an object in free fall. Which conclusion can be made from the model? (1 point) Responses The kinetic energy stays the same over time. The kinetic energy stays the same over time. The potential energy stays the same over time. The potential energy stays the same over time. The total energy stays the same over time. The total energy stays the same over time. The velocity stays the same over time
In a computational model where an object is in free fall under the influence of gravity, assuming there is no air resistance, the following physical principles apply:
1. The kinetic energy of the object will increase over time, as velocity increases due to the acceleration caused by gravity.
2. The potential energy of the object will decrease over time, as height from the ground decreases while the object falls.
3. The total mechanical energy (sum of kinetic and potential energy) stays the same over time, due to the conservation of energy.
4. The velocity of the object increases over time, again, due to the acceleration caused by gravity.
Now, using these principles:
- "The kinetic energy stays the same over time." - This is incorrect because kinetic energy increases as the object accelerates during its fall.
- "The potential energy stays the same over time." - This is incorrect because potential energy decreases as the object falls and its height above the ground decreases.
- "The total energy stays the same over time." - This is correct if we are ignoring air resistance and other non-conservative forces, as energy is conserved in a closed system.
- "The velocity stays the same over time." - This is incorrect because velocity increases due to the gravitational acceleration until terminal velocity is reached if air resistance is factored in. However, in an ideal model without air resistance, the velocity would continue to increase.
Therefore, for the question about the conclusion that can be made from the computational model of energy changes experienced by an object in free fall, the correct response is:
"The total energy stays the same over time."
This statement is based on the principle of conservation of mechanical energy in a closed system where there is no air resistance.
According to a computational model, which statement describes the effect decreasing the initial height of an object in free fall will have on the object?(1 point) Responses The initial potential energy of the object will be greater. The initial potential energy of the object will be greater. The final velocity of the object will remain the same. The final velocity of the object will remain the same. The total energy of the object will decrease. The total energy of the object will decrease. The total energy of the object will remain the same
In the context of free fall, when you decrease the initial height of an object, here are the effects on the object's energy and velocity:
- Decreasing the initial height of the object means that there is less distance for the object to fall, which reduces the object's initial gravitational potential energy because potential energy (PE) is given by PE = mgh (where m is mass, g is the acceleration due to gravity, and h is height).
- The final velocity of the object will not remain the same if the initial height changes. A lower initial height means the object has less time to accelerate under gravity before reaching the ground, resulting in a lower final velocity.
- The total energy of the object at the beginning includes its initial potential energy. Since the potential energy is proportional to height (PE = mgh), when you decrease the initial height, the initial total energy is also decreased.
- The total energy of the object while falling would remain the same if no external forces like air resistance are present, as per the conservation of energy. However, the initial total energy (sum of initial potential and kinetic energy, assuming the object starts at rest) will be less with decreased height because the potential energy is reduced.
Given the above explanations, the correct statement describing the effect of decreasing the initial height of an object in free fall on the object is:
"The total energy of the object will decrease."
This is due to the initial potential energy being lower as a result of the reduced height.
According to a computational model of the energy change in a pendulum, what will happen if the mass of the pendulum increases?(1 point) Responses The initial potential energy will increase. The initial potential energy will increase. The initial kinetic energy will increase. The initial kinetic energy will increase. The initial angular velocity will increase. The initial angular velocity will increase. The initial release angle will increase.
In a pendulum system, the mass of the pendulum affects its potential energy, provided that the height from which the pendulum is released is not changed. The potential energy (PE) of a pendulum at a given height is calculated using the formula PE = mgh, where m represents the mass of the pendulum, g is the acceleration due to gravity, and h is the height above the lowest point of the pendulum's swing.
So, if the mass (m) of the pendulum increases and the height (h) and acceleration due to gravity (g) remain constant, the potential energy (PE) of the pendulum will increase accordingly because PE is directly proportional to mass.
The kinetic energy (KE) of the pendulum is not directly dependent on the mass at the initial state since a pendulum at its highest point (initial release) has its kinetic energy at zero (assuming it starts from rest). Kinetic energy is calculated with the formula KE = 0.5mv², where v is velocity; at the topmost point of the swing, v is initially zero.
The angular velocity and the release angle are not directly influenced by the mass of the pendulum. The angular velocity depends on the length of the pendulum and the force of gravity, and the initial release angle is a separate, independent condition that sets the amplitude of the swing but does not depend on the mass.
Given the choices provided, the correct statement related to what will happen if the mass of the pendulum increases is:
"The initial potential energy will increase."
This is the only effect that an increase in mass has among the options listed.