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Original Question
Two rockets with the same mass are accelerated. Rocket A accelerates twice as quickly as rocket B. Which statement is correct?(...Question
Two rockets with the same mass are accelerated. Rocket A accelerates twice as quickly as rocket B. Which statement is correct?(1 point)
Responses
The motor in rocket A is half as powerful as the motor in rocket B.
The motor in rocket A is half as powerful as the motor in rocket B.
The motor in rocket A is twice as powerful as the motor in rocket B.
The motor in rocket A is twice as powerful as the motor in rocket B.
The motor in rocket A is four times as powerful as the motor in rocket B.
The motor in rocket A is four times as powerful as the motor in rocket B.
The motor in rocket A is equally as powerful
Responses
The motor in rocket A is half as powerful as the motor in rocket B.
The motor in rocket A is half as powerful as the motor in rocket B.
The motor in rocket A is twice as powerful as the motor in rocket B.
The motor in rocket A is twice as powerful as the motor in rocket B.
The motor in rocket A is four times as powerful as the motor in rocket B.
The motor in rocket A is four times as powerful as the motor in rocket B.
The motor in rocket A is equally as powerful
Answers
Answer
A model rocket has a mass of 0.2 kg, with a motor that can provide a force of 100 N. A second model rocket is being built with the same motor, but it is being designed to accelerate half as much as the first rocket. What kind of change can be made in the design to achieve this objective? (1 point)
Responses
The mass of the second rocket should be 0.2 kg.
The mass of the second rocket should be 0.2 kg.
The mass of the second rocket should be 0.01 kg.
The mass of the second rocket should be 0.01 kg.
The mass of the second rocket should be 0.4 kg.
The mass of the second rocket should be 0.4 kg.
The mass of the second
Responses
The mass of the second rocket should be 0.2 kg.
The mass of the second rocket should be 0.2 kg.
The mass of the second rocket should be 0.01 kg.
The mass of the second rocket should be 0.01 kg.
The mass of the second rocket should be 0.4 kg.
The mass of the second rocket should be 0.4 kg.
The mass of the second
Answer
Five motorboats are being tested to see which reaches the highest velocity in the same amount of time. After graphing the acceleration versus force for each motorboat, the graph is a sloped line with a y-intercept of zero. Which statement is correct about these motorboats?(1 point)
Responses
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass
Responses
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass
Answer
If a soccer ball’s mass is 5 kg and a player who weighs 50 kg kicks the soccer ball forward with a force of 5 N , how much force does the ball exert on the player’s foot and in what direction?(1 point)
Responses
10 kg/N backward
10 kg/N backward
5 N backward
5 N backward
100 kg forward
100 kg forward
5
Responses
10 kg/N backward
10 kg/N backward
5 N backward
5 N backward
100 kg forward
100 kg forward
5
Answer
A toy helicopter flies forward with a force of 15 N into an oncoming wind of 10 N. The force of gravity pulls the helicopter down with a force of 5 N, but the propeller is providing an upward force of 10 N.
Which of the following accurately describes the helicopter’s force?
(1 point)
Responses
The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.
The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.
The toy helicopter
Which of the following accurately describes the helicopter’s force?
(1 point)
Responses
The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.
The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.
The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.
The toy helicopter
Answered by
GPT-4o mini
To determine the relationship between the accelerations and the powers of the rockets, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of that object times its acceleration (F = m * a).
Let:
- The mass of both rockets be \( m \).
- The acceleration of rocket A be \( a_A \) (which is twice that of rocket B, so \( a_A = 2a_B \)).
- The acceleration of rocket B be \( a_B \).
According to Newton's second law:
- The force applied by the motor of rocket A is \( F_A = m \cdot a_A \).
- The force applied by the motor of rocket B is \( F_B = m \cdot a_B \).
Since \( a_A = 2a_B \), we can express the forces in terms of the accelerations:
\[
F_A = m \cdot (2a_B) = 2m \cdot a_B
\]
\[
F_B = m \cdot a_B
\]
To relate the power developed by the motors, we can use the equation for power, which is given by \( P = F \cdot v \) (force times the velocity of the object). However, since we want to relate the powers without specific velocities, we can simply consider the forces exerted by both motors.
Given that the mass is the same for both rockets and the acceleration of rocket A is twice that of rocket B, we have:
\[
F_A = 2F_B
\]
The motor power is not directly determined by just acceleration, but since force (and hence power) is proportional to acceleration for the same mass, we can conclude:
\[
P_A \propto F_A = 2F_B \propto P_B
\]
Thus, the power of rocket A's motor is twice the power of rocket B's motor. Therefore, the correct statement is:
**The motor in rocket A is twice as powerful as the motor in rocket B.**
Let:
- The mass of both rockets be \( m \).
- The acceleration of rocket A be \( a_A \) (which is twice that of rocket B, so \( a_A = 2a_B \)).
- The acceleration of rocket B be \( a_B \).
According to Newton's second law:
- The force applied by the motor of rocket A is \( F_A = m \cdot a_A \).
- The force applied by the motor of rocket B is \( F_B = m \cdot a_B \).
Since \( a_A = 2a_B \), we can express the forces in terms of the accelerations:
\[
F_A = m \cdot (2a_B) = 2m \cdot a_B
\]
\[
F_B = m \cdot a_B
\]
To relate the power developed by the motors, we can use the equation for power, which is given by \( P = F \cdot v \) (force times the velocity of the object). However, since we want to relate the powers without specific velocities, we can simply consider the forces exerted by both motors.
Given that the mass is the same for both rockets and the acceleration of rocket A is twice that of rocket B, we have:
\[
F_A = 2F_B
\]
The motor power is not directly determined by just acceleration, but since force (and hence power) is proportional to acceleration for the same mass, we can conclude:
\[
P_A \propto F_A = 2F_B \propto P_B
\]
Thus, the power of rocket A's motor is twice the power of rocket B's motor. Therefore, the correct statement is:
**The motor in rocket A is twice as powerful as the motor in rocket B.**
Answered by
GPT-4o mini
To analyze how to achieve the desired acceleration for the second rocket, we can again refer to Newton's second law of motion, \( F = m \cdot a \).
For the first rocket:
- Mass \( m_1 = 0.2 \, \text{kg} \)
- Force \( F = 100 \, \text{N} \)
To find the acceleration of the first rocket, we can rearrange the formula:
\[
a_1 = \frac{F}{m_1} = \frac{100 \, \text{N}}{0.2 \, \text{kg}} = 500 \, \text{m/s}^2
\]
The second rocket is designed to accelerate half as much as the first rocket, so:
\[
a_2 = \frac{a_1}{2} = \frac{500 \, \text{m/s}^2}{2} = 250 \, \text{m/s}^2
\]
Now using the same force from the motor (100 N) for the second rocket, we can find the required mass \( m_2 \) to achieve this new acceleration:
\[
F = m_2 \cdot a_2
\]
Rearranging gives:
\[
m_2 = \frac{F}{a_2} = \frac{100 \, \text{N}}{250 \, \text{m/s}^2} = 0.4 \, \text{kg}
\]
This means that to achieve an acceleration of 250 m/s² (which is half of the acceleration of the first rocket), the mass of the second rocket should be increased to 0.4 kg.
Thus, the correct change to make in the design is:
**The mass of the second rocket should be 0.4 kg.**
For the first rocket:
- Mass \( m_1 = 0.2 \, \text{kg} \)
- Force \( F = 100 \, \text{N} \)
To find the acceleration of the first rocket, we can rearrange the formula:
\[
a_1 = \frac{F}{m_1} = \frac{100 \, \text{N}}{0.2 \, \text{kg}} = 500 \, \text{m/s}^2
\]
The second rocket is designed to accelerate half as much as the first rocket, so:
\[
a_2 = \frac{a_1}{2} = \frac{500 \, \text{m/s}^2}{2} = 250 \, \text{m/s}^2
\]
Now using the same force from the motor (100 N) for the second rocket, we can find the required mass \( m_2 \) to achieve this new acceleration:
\[
F = m_2 \cdot a_2
\]
Rearranging gives:
\[
m_2 = \frac{F}{a_2} = \frac{100 \, \text{N}}{250 \, \text{m/s}^2} = 0.4 \, \text{kg}
\]
This means that to achieve an acceleration of 250 m/s² (which is half of the acceleration of the first rocket), the mass of the second rocket should be increased to 0.4 kg.
Thus, the correct change to make in the design is:
**The mass of the second rocket should be 0.4 kg.**
Answered by
GPT-4o mini
Given the information that the graph of acceleration versus force for the five motorboats is a sloped line with a y-intercept of zero, we can analyze the implications of this graph.
According to Newton's second law of motion, the relationship between force \( (F) \), mass \( (m) \), and acceleration \( (a) \) is given by:
\[
F = m \cdot a
\]
This can be rearranged to express acceleration in terms of force and mass:
\[
a = \frac{F}{m}
\]
From this relationship, we see that if the graph of acceleration (y-axis) versus force (x-axis) is a straight line through the origin, it indicates a linear relationship between force and acceleration. The slope of this line will represent the reciprocal of the mass (i.e., \( \frac{1}{m} \)).
If the slopes of the lines for all five motorboats are the same, it means they have the same mass. If the slopes of the lines differ, then they have different masses. However, since it is mentioned that the graph shows a single sloped line, we can infer that all five motorboats indeed must have the same mass.
Therefore, the correct statement is:
**All five motorboats have the same mass.**
According to Newton's second law of motion, the relationship between force \( (F) \), mass \( (m) \), and acceleration \( (a) \) is given by:
\[
F = m \cdot a
\]
This can be rearranged to express acceleration in terms of force and mass:
\[
a = \frac{F}{m}
\]
From this relationship, we see that if the graph of acceleration (y-axis) versus force (x-axis) is a straight line through the origin, it indicates a linear relationship between force and acceleration. The slope of this line will represent the reciprocal of the mass (i.e., \( \frac{1}{m} \)).
If the slopes of the lines for all five motorboats are the same, it means they have the same mass. If the slopes of the lines differ, then they have different masses. However, since it is mentioned that the graph shows a single sloped line, we can infer that all five motorboats indeed must have the same mass.
Therefore, the correct statement is:
**All five motorboats have the same mass.**
Answered by
GPT-4o mini
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that when the player kicks the soccer ball, the ball will exert an equal force back on the player's foot in the opposite direction.
In this case, the player exerts a force of 5 N forward on the soccer ball. Therefore, the soccer ball will exert a force of 5 N backward on the player's foot.
The correct answer is:
**5 N backward.**
In this case, the player exerts a force of 5 N forward on the soccer ball. Therefore, the soccer ball will exert a force of 5 N backward on the player's foot.
The correct answer is:
**5 N backward.**
Answered by
GPT-4o mini
To analyze the forces acting on the toy helicopter, we need to consider both the forward and vertical forces.
**Forward Forces:**
- The helicopter flies forward with a force of 15 N.
- There is an oncoming wind that exerts a force of 10 N in the opposite direction.
The **net forward force** can be calculated as follows:
\[
\text{Net forward force} = \text{Forward force} - \text{Wind force} = 15 \, \text{N} - 10 \, \text{N} = 5 \, \text{N}
\]
So, the helicopter is effectively flying forward with a force of 5 N.
**Vertical Forces:**
- The force of gravity pulling the helicopter downward is 5 N.
- The propeller is providing an upward force of 10 N.
The **net vertical force** can be calculated as follows:
\[
\text{Net upward force} = \text{Upward force} - \text{Gravity} = 10 \, \text{N} - 5 \, \text{N} = 5 \, \text{N}
\]
So, the helicopter is effectively rising upward with a force of 5 N.
Putting these calculations together, we find:
- The toy helicopter is flying forward with a net force of 5 N.
- The toy helicopter is flying upward with a net force of 5 N.
Thus, the correct statement is:
**The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.**
**Forward Forces:**
- The helicopter flies forward with a force of 15 N.
- There is an oncoming wind that exerts a force of 10 N in the opposite direction.
The **net forward force** can be calculated as follows:
\[
\text{Net forward force} = \text{Forward force} - \text{Wind force} = 15 \, \text{N} - 10 \, \text{N} = 5 \, \text{N}
\]
So, the helicopter is effectively flying forward with a force of 5 N.
**Vertical Forces:**
- The force of gravity pulling the helicopter downward is 5 N.
- The propeller is providing an upward force of 10 N.
The **net vertical force** can be calculated as follows:
\[
\text{Net upward force} = \text{Upward force} - \text{Gravity} = 10 \, \text{N} - 5 \, \text{N} = 5 \, \text{N}
\]
So, the helicopter is effectively rising upward with a force of 5 N.
Putting these calculations together, we find:
- The toy helicopter is flying forward with a net force of 5 N.
- The toy helicopter is flying upward with a net force of 5 N.
Thus, the correct statement is:
**The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.**