A dog weighing 18 kg runs into a park at a velocity of .63 m/s. What is the momentum of the dog?

Question

Responses

17.37 kg*m/s

.035 kg*m/s

11.34 kg*m/s

28.5 kg*m/s

Answer 1

Momentum (p) is calculated using the formula:

\[ p = m \times v \]

where:

• \(m\) is the mass in kilograms,
• \(v\) is the velocity in meters per second.

In this case, the mass of the dog is 18 kg and its velocity is 0.63 m/s.

Now, substituting the values:

\[ p = 18 , \text{kg} \times 0.63 , \text{m/s} = 11.34 , \text{kg*m/s} \]

Therefore, the momentum of the dog is 11.34 kg*m/s.

Answer 2

A spring scale shows a net force of 0.8 N acting on a 1.5-kg mass. What happens to the acceleration of the object if the net force is decreased to 0.2 N?
Responses

The acceleration increases to four times its original value, or about 0.13 m/s2.

The acceleration increases to four times its original value, or about 2.13 m/s2.

The acceleration decreases to a quarter of its original value, or about 0.13 m/s2.

The acceleration decreases to a quarter of its original value, or about 2.13 m/s2.

Answer 3

To find the acceleration of the object, we can use Newton's second law of motion, which states:

\[ F = m \times a \]

where:

• \(F\) is the net force,
• \(m\) is the mass,
• \(a\) is the acceleration.

1. First, we calculate the original acceleration with the net force of 0.8 N.

Given:

• \(F = 0.8 , \text{N}\)
• \(m = 1.5 , \text{kg}\)

Using the formula to find acceleration \(a\):

\[ a = \frac{F}{m} \]

Substituting in the values:

\[ a = \frac{0.8 , \text{N}}{1.5 , \text{kg}} \approx 0.533 , \text{m/s}^2 \]

2. Next, we calculate the new acceleration when the net force is decreased to 0.2 N.

Given:

• \(F = 0.2 , \text{N}\)

Using the same formula:

\[ a = \frac{F}{m} = \frac{0.2 , \text{N}}{1.5 , \text{kg}} \approx 0.133 , \text{m/s}^2 \]

3. Now, we compare the two accelerations:

• Original acceleration: \(0.533 , \text{m/s}^2\)
• New acceleration: \(0.133 , \text{m/s}^2\)

To find the relationship:

\[ \text{New acceleration} = \frac{0.2}{0.8} \times \text{Original acceleration} = \frac{1}{4} \times 0.533 \approx 0.133 , \text{m/s}^2 \]

This means the acceleration decreases to a quarter of its original value.

Thus, the correct response is:

The acceleration decreases to a quarter of its original value, or about 0.13 m/s².

Answer 4

Use the graph of velocity vs. time for an object to answer the question

Which statement fairly compares segment 2 and segment 3?

Responses

Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3.

Segments 2 and 3 have different periods of time and the force during segment 2 is different than the force during segment 3.

Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time.

Segments 2 and 3 have equal periods of time and the force acting in each segment is the same during each period of time.

Answer 5

To accurately analyze which statement fairly compares segment 2 and segment 3 of the velocity vs. time graph, you would typically look for the following key aspects:

1. Periods of time - Compare the lengths of segments 2 and 3 on the time axis.
2. Force - Determine whether the slope of the segments (which indicates acceleration) is the same or different. The force acting on an object is related to its acceleration (F = m * a). If the slopes are the same, the forces are equivalent, assuming the mass of the object remains constant.

Since I don’t have access to the actual graph, I will outline the interpretations based on the potential conditions:

• If segments 2 and 3 have equal lengths on the time axis (meaning they last for the same time) and their slopes (acceleration) are both different, then the correct response would be:

  • "Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3."

• If segments 2 and 3 have different lengths on the time axis and their slopes are different, then the correct response would be:

  • "Segments 2 and 3 have different periods of time and the force during segment 2 is different than the force during segment 3."

• If segments 2 and 3 have different lengths on the time axis but their slopes are the same, the correct response would be:

  • "Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time."

• If segments 2 and 3 have equal lengths on the time axis and the slopes are the same, you would select:

  • "Segments 2 and 3 have equal periods of time and the force acting in each segment is the same during each period of time."

To conclude, without the visual reference to the graph, you would need to check these two criteria (length of segments and slopes) to choose the appropriate comparison statement. Please assess the graph accordingly to make the final determination.

Answer 6

Which quantity or quantities is/are increasing for the object represented by Line B?

Responses

velocity, position, and acceleration

velocity and position

velocity and acceleration

velocity only

Answer 7

To determine which quantity or quantities are increasing for the object represented by Line B on a velocity vs. time graph, we need to analyze the characteristics of the graph:

1. Velocity: If Line B slopes upwards, it indicates that the velocity is increasing over time. If it is flat, the velocity is constant, and if it slopes downwards, the velocity is decreasing.

2. Position: Position increases when the velocity is positive. If Line B indicates increasing velocity (i.e., it slopes upwards), then position will also be increasing.

3. Acceleration: Acceleration is represented by the slope of the velocity vs. time graph. If Line B has a constant positive slope, acceleration is positive and increasing given a constant positive velocity. If Line B has a changing slope, it may affect the acceleration differently.

Given these principles, here are the implications of the options:

• If Line B slopes upwards (indicating an increase in velocity), then both velocity and position are increasing if time progresses as well, since the object is moving forward.
• If the slope indicates a change in the steepness (constantly increasing slope), then acceleration is also increasing.

Based solely on common interpretations of the graph, if Line B shows an increasing slope (implying the object is accelerating), then we can conclude that velocity and position are increasing, and potentially acceleration too.

Based on your options, if we are sticking to the simplest view considering an upward sloping Line B, the best situational response would be:

"velocity and position."

If Line B indicates that the slope is increasing (implying increasing acceleration), the more comprehensive answer could potentially include acceleration as well. But from the options you've provided, "velocity and position" seems to fit best for typical context.

To conclude correctly, please refer to the specific characteristics of Line B in the graph!

Answer 8

The same type of engine is placed in two different airplanes. The first airplane is twice as heavy as the second airplane. Which statement is correct about the mass of the airplane and its acceleration, assuming a constant net force?
Responses

Increasing the acceleration of the airplane causes the engine to provide less force.

Increasing the acceleration of the airplane causes the engine to provide more force.

Decreasing the mass of the airplane will result in the airplane accelerating more.

Decreasing the mass of the airplane will result in the airplane accelerating less.

Answer 9

To analyze the relationship between mass, acceleration, and net force, we can refer to Newton's second law of motion, which states:

\[ F = m \times a \]

where:

• \(F\) is the net force,
• \(m\) is the mass,
• \(a\) is the acceleration.

Given the scenario:

• The first airplane is twice as heavy as the second airplane. Let's denote the mass of the second airplane as \(m\) and the mass of the first airplane as \(2m\).

Analyzing the Options

1. Increasing the acceleration of the airplane causes the engine to provide less force.

   • This statement is incorrect. If the acceleration increases while the mass stays the same, the required force (from the engine) must also increase to maintain the relationship \(F = m \times a\).

2. Increasing the acceleration of the airplane causes the engine to provide more force.

   • This statement is correct. If you want to increase the acceleration (assuming mass remains constant), the engine must provide more force.

3. Decreasing the mass of the airplane will result in the airplane accelerating more.

   • This statement is also correct. If the mass decreases while the net force is held constant, then acceleration increases, as described by the rearranged formula \(a = \frac{F}{m}\). A smaller \(m\) results in a larger \(a\).

4. Decreasing the mass of the airplane will result in the airplane accelerating less.

   • This statement is incorrect. As previously stated, decreasing mass leads to increased acceleration (if force is constant).

Conclusion

• The correct statements are:
  • "Increasing the acceleration of the airplane causes the engine to provide more force."
  • "Decreasing the mass of the airplane will result in the airplane accelerating more."

If you need to choose just one statement from the options provided that captures the essence of the relationship considering the constant net force, the best response would be:

"Increasing the acceleration of the airplane causes the engine to provide more force."

Answer 10

The harder a gas pedal in a car is pressed, the faster the car’s velocity increases. Which phrase best describes the relationship between how hard the gas pedal is pressed and the acceleration of the car? Responses:

There is both a negative correlation and causation.

There is a negative correlation but no causation.

There is a positive correlation but no causation.

There is both a positive correlation and causation.

Answer 11

To analyze the relationship between how hard the gas pedal is pressed and the acceleration of the car, we can assess the statements provided:

1. Correlation refers to the relationship between two variables—how one may change in relation to the other.
2. Causation implies that one variable directly affects the other.

In the context of pressing the gas pedal:

• As the gas pedal is pressed harder (first variable), the acceleration of the car (second variable) increases. This suggests a direct relationship between pressing the gas pedal and the resulting acceleration of the car.

Evaluating the Options:

1. There is both a negative correlation and causation.

   • This is incorrect. A negative correlation would mean that as one variable increases, the other decreases, which does not apply here.

2. There is a negative correlation but no causation.

   • This is incorrect. Again, this suggests that as one variable increases, the other decreases, which is not the case.

3. There is a positive correlation but no causation.

   • This is incorrect because, while there is a positive correlation, pressing the gas pedal does indeed cause an increase in acceleration, so there is causation as well.

4. There is both a positive correlation and causation.

   • This is correct. As the gas pedal is pressed harder (increased input), the car’s acceleration increases, demonstrating both a positive correlation and causation.

Conclusion

The best phrase that describes the relationship between how hard the gas pedal is pressed and the acceleration of the car is:

"There is both a positive correlation and causation."