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The same motor is used in rockets with different masses. The rockets have different accelerations. According to Newton’s second law, how is acceleration expected to change as the rocket mass increases

Responses:

Acceleration cannot be predicted based on changes in mass.

As rocket mass increases, acceleration increases.

As rocket mass increases, acceleration decreases.

There are no changes in acceleration, as it would depend on the amount of force.

11 answers

According to Newton's second law of motion, acceleration (a) is directly proportional to the net force (F) acting on an object and inversely proportional to the mass (m) of the object, expressed by the equation \( F = m \cdot a \).

If we rearrange this equation to express acceleration, we get:

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

From this, we can see that as the mass (m) of the rocket increases while the force (F) provided by the motor remains constant, the acceleration (a) will decrease. Therefore, the correct response is:

As rocket mass increases, acceleration decreases.

Different amounts of force are applied to the same boat over several trials, and the acceleration is measured. In a graph of acceleration versus net force, what does the slope of the graph represent
Responses:

the inverse of the speed of the boat

the inverse of the mass of the boat

the mass of the boat

the speed of the boat

In the context of Newton's second law, \( F = m \cdot a \), if we rearrange it to express acceleration in terms of net force and mass, we have:

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

When you plot acceleration (a) on the y-axis and net force (F) on the x-axis, the relationship can be expressed as:

\[ a = \frac{1}{m} \cdot F \]

In this linear equation, the slope of the graph (change in acceleration per change in force) is equal to \( \frac{1}{m} \), which is the inverse of the mass of the boat.

Therefore, the correct response is:

the inverse of the mass of the boat.

Several motorboats with the same mass are used in an experiment. The forces of the different motors versus their accelerations are graphed. What is the y-intercept of this graph?
Responses:

the inverse of the mass

the mass

the velocity

zero

In the context of the relationship derived from Newton's second law, \( F = m \cdot a \), if you rearrange the equation to express force in terms of mass and acceleration, you have:

\[ F = m \cdot a \]

When you plot the force (F) on the y-axis and acceleration (a) on the x-axis, the equation can be expressed as:

\[ F = m \cdot a \]

This is a linear equation where the slope is the mass (m), and there is no constant term, which means that when the acceleration (a) is zero, the force (F) is also zero.

Thus, the y-intercept of this graph, where acceleration is zero, is at the point where both force and acceleration equal zero.

So, the correct response is:

zero.

Which situation describes an object that is accelerating
Responses:

when the velocity increases

when the net force is zero

when equal forces act simultaneously

when the velocity is constant

Acceleration refers to any change in the velocity of an object, which includes an increase or decrease in speed, or a change in direction. Given the response options:

  1. When the velocity increases - This clearly indicates that the object is accelerating, as an increase in velocity means a change in speed.

  2. When the net force is zero - This means the object is either at rest or moving at a constant velocity, implying no acceleration.

  3. When equal forces act simultaneously - If equal forces are acting on an object in opposite directions, the net force is zero, meaning no acceleration occurs.

  4. When the velocity is constant - This indicates that there is no change in speed or direction, so the object is not accelerating.

Based on the definitions, the correct response describing an object that is accelerating is:

when the velocity increases.

Antonio Stradivari is famous for making

Responses

excellent string instruments.

a flute that could play in multiple keys.

a brass instrument with valves for additional range.

a foot pedal for tuning timpani.

Antonio Stradivari is famous for making:

excellent string instruments.

He is particularly renowned for his violins, but he also crafted other string instruments like cellos and guitars. Stradivari's instruments are highly regarded for their craftsmanship and quality of sound.

When the vibrating column of air inside a woodwind or brass instrument is made longer, the pitch

Responses:

gets higher.

gets lower.

stays the same.

can no longer be determined.

When the vibrating column of air inside a woodwind or brass instrument is made longer, the pitch:

gets lower.

This is because a longer column of air results in a lower frequency of vibration, which produces a lower pitch. Conversely, shortening the column increases the frequency and raises the pitch.