Student Depth of Object in Sand (cm)

Question

Maddie 1.8
Naveed 4.0
Two students drop an object into sand from a height of 1.5 meters. They record the depth of the hole made in the sand by each student’s object. What is the most likely explanation for the results?

(1 point)
Responses

Naveed’s object has less mass.
Naveed’s object has less mass.

Maddie’s object has a smaller width.
Maddie’s object has a smaller width.

Naveed’s object had greater kinetic energy.
Naveed’s object had greater kinetic energy.

Maddie’s object had a faster drop speed.

Answer 1

The most likely explanation for the results is:

Naveed’s object had greater kinetic energy.

When objects are dropped, their kinetic energy when they hit the ground is related to their mass and the height from which they are dropped. Since Naveed's object caused a greater depth in the sand, it suggests that it had more kinetic energy upon impact, which could be due to it having a greater mass or being influenced by other factors such as shape or material.

Answer 2

A student wants to determine the effect of mass on kinetic energy. She will drop two balls of the same size into a pool of water. Which investigation method should the student use?(1 point)
Responses

She should drop two balls with different masses from the same height.
She should drop two balls with different masses from the same height.

She should drop two balls with different masses from different heights.
She should drop two balls with different masses from different heights.

She should drop two balls of the same mass from different heights.
She should drop two balls of the same mass from different heights.

She should drop two balls of the same mass from the same height.

Answer 3

The correct investigation method for the student to determine the effect of mass on kinetic energy is:

She should drop two balls with different masses from the same height.

This method allows the student to isolate the variable of mass while keeping the height consistent. Since kinetic energy is determined by the formula \( KE = \frac{1}{2} mv^2 \) (where \( m \) is mass and \( v \) is velocity), dropping the balls from the same height will ensure that they have the same drop speed (assuming air resistance is negligible), allowing for a clear comparison of how mass affects kinetic energy.

Answer 4

Which falling object will result in the least kinetic energy when it collides with the ground?(1 point)
Responses

100 grams of water falling at 10 m/s
100 grams of water falling at 10 m/s

10 grams of water falling at 1 m/s
10 grams of water falling at 1 m/s

10 grams of dirt falling at 2 m/s
10 grams of dirt falling at 2 m/s

100 grams of dirt falling at 15 m/s

Answer 5

To determine which falling object will result in the least kinetic energy when it collides with the ground, we can use the formula for kinetic energy (KE):

\[ KE = \frac{1}{2} mv^2 \]

Where:

• \( m \) is the mass of the object in kilograms
• \( v \) is the velocity of the object in meters per second

Now, let's calculate the kinetic energy for each option:

1. 100 grams of water falling at 10 m/s

   • Mass = 0.1 kg, Velocity = 10 m/s
   • \( KE = \frac{1}{2} (0.1)(10^2) = 0.5 \times 0.1 \times 100 = 5 , \text{Joules} \)

2. 10 grams of water falling at 1 m/s

   • Mass = 0.01 kg, Velocity = 1 m/s
   • \( KE = \frac{1}{2} (0.01)(1^2) = 0.5 \times 0.01 \times 1 = 0.005 , \text{Joules} \)

3. 10 grams of dirt falling at 2 m/s

   • Mass = 0.01 kg, Velocity = 2 m/s
   • \( KE = \frac{1}{2} (0.01)(2^2) = 0.5 \times 0.01 \times 4 = 0.02 , \text{Joules} \)

4. 100 grams of dirt falling at 15 m/s

   • Mass = 0.1 kg, Velocity = 15 m/s
   • \( KE = \frac{1}{2} (0.1)(15^2) = 0.5 \times 0.1 \times 225 = 11.25 , \text{Joules} \)

Based on these calculations, the object that results in the least kinetic energy when it collides with the ground is:

10 grams of water falling at 1 m/s (0.005 Joules).

Answer 6

This image of a roller coaster is designed to show important information about potential and kinetic energy. One of these labeled pieces of information is incorrect. Which information is wrong, and why?

(1 point)
Responses

The roller coaster would only have kinetic energy at the point labeled “gravitational potential energy and kinetic energy.”
The roller coaster would only have kinetic energy at the point labeled “gravitational potential energy and kinetic energy.”

The roller coaster would only have potential energy at the point labeled “gravitational potential energy and kinetic energy.”
The roller coaster would only have potential energy at the point labeled “gravitational potential energy and kinetic energy.”

The spot marked “maximum gravitational potential energy” should be on the lowest point of the roller coaster, at the far left side on the bottom.
The spot marked “maximum gravitational potential energy” should be on the lowest point of the roller coaster, at the far left side on the bottom.

The spot with the “maximum kinetic energy” should be on the lowest point of the roller coaster, at the far left side on the bottom.

Answer 7

The incorrect piece of information is:

The roller coaster would only have kinetic energy at the point labeled “gravitational potential energy and kinetic energy.”

This statement is wrong because at any given point on a roller coaster, both potential energy (due to height) and kinetic energy (due to motion) can exist simultaneously. When the roller coaster is moving, even if it's at a height where it still has potential energy, it will also have some kinetic energy.

To clarify the other options:

• The point labeled “maximum gravitational potential energy” should be at the highest point of the roller coaster, not the lowest point.
• The point marked with the “maximum kinetic energy” should indeed be at the lowest point of the roller coaster, where the speed is highest, and potential energy is lowest.

Therefore, the first statement is the one that is incorrect.

Answer 8

Four rivers have the same volume of water flow over time but fall from different heights to power hydroelectric dams. Which dam would provide the most hydroelectric power?(1 point)
Responses

dam A: fall height of 175 feet
dam A: fall height of 175 feet

dam B: fall height of 75 feet
dam B: fall height of 75 feet

dam C: fall height of 135 feet
dam C: fall height of 135 feet

dam D: fall height of 100 feet

Answer 9

To determine which dam would provide the most hydroelectric power among the options provided, we can consider the relationship between the height of the water fall and the potential energy that can be converted into electrical energy.

The potential energy (PE) of the water at a certain height is calculated using the formula:

\[ PE = mgh \]

Where:

• \( m \) is the mass of the water
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
• \( h \) is the height of the fall

Since all dams have the same volume of water flow (and thus the same mass if we account for time), the potential energy—and therefore the power output—will depend primarily on the height of the water fall. The higher the fall, the more potential energy is available to be converted into hydroelectric power.

Given the heights provided:

• Dam A: 175 feet
• Dam B: 75 feet
• Dam C: 135 feet
• Dam D: 100 feet

Dam A, with a fall height of 175 feet, will provide the most hydroelectric power because it has the greatest potential energy due to its higher height compared to the other dams.

Therefore, the answer is:

Dam A: fall height of 175 feet.