A billiard ball moves with 3 kg⋅m/s of momentum and strikes three other billiard balls. What is the total momentum of the balls after the collision?
To find the total momentum after the collision, we need to consider the momentum of each individual ball before and after the collision.
Let's assume the initial momentum of the first billiard ball is 3 kg⋅m/s.
Let's assume the momentum of the second billiard ball after the collision is x kg⋅m/s.
Let's assume the momentum of the third billiard ball after the collision is y kg⋅m/s.
Let's assume the momentum of the fourth billiard ball after the collision is z kg⋅m/s.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
So, 3 kg⋅m/s = 3 kg⋅m/s + x kg⋅m/s + y kg⋅m/s + z kg⋅m/s
Simplifying the equation, we get:
0 kg⋅m/s = x kg⋅m/s + y kg⋅m/s + z kg⋅m/s
Since there is no initial momentum for the other three balls, the total momentum after the collision is 0 kg⋅m/s.
Momentum Quick Check%0D%0A1 of 51 of 5 Items%0D%0A%0D%0AQuestion%0D%0AA billiard ball moves with 3 kg⋅m/s of momentum and strikes three other billiard balls. What is the total momentum of the balls after the collision?(1 point)%0D%0AResponses%0D%0A%0D%0A3 kg⋅m/s%0D%0A3 kilograms times meters per second%0D%0A%0D%0Aless than 3 kg⋅m/s%0D%0Aless than 3 kilograms times meters per second%0D%0A%0D%0Amore than 3 kg⋅m/s%0D%0Amore than 3 kilograms times meters per second%0D%0A%0D%0AIt depends on the mass of each ball.
The total momentum of the balls after the collision depends on the mass of each ball. Therefore, the correct response is "It depends on the mass of each ball."
A small rock bounces off the windshield of a moving car and experiences a large change in velocity. How does the car’s momentum change?(1 point)%0D%0AResponses%0D%0A%0D%0AIt has a change in momentum equal to that of the rock, in the opposite direction.%0D%0AIt has a change in momentum equal to that of the rock, in the opposite direction.%0D%0A%0D%0AIt has a change in momentum greater than that of the rock, in the opposite direction.%0D%0AIt has a change in momentum greater than that of the rock, in the opposite direction.%0D%0A%0D%0AIt does not change.%0D%0AIt does not change.%0D%0A%0D%0AIt has a much smaller change in momentum than that of the rock, in the opposite direction.
The correct response is: "It has a change in momentum equal to that of the rock, in the opposite direction."
Momentum Quick Check%0D%0A3 of 53 of 5 Items%0D%0A%0D%0AQuestion%0D%0AAn object has a mass of 5 kg and a velocity of 20 m/s. What is the momentum of the object?(1 point)%0D%0AResponses%0D%0A%0D%0A100 kg⋅m/s%0D%0A100 kilograms times meters per second%0D%0A%0D%0A25 kg⋅m/s%0D%0A25 kilograms times meters per second%0D%0A%0D%0A0.25 kg⋅m/s%0D%0A0 point 2 5 kilograms times meters per second%0D%0A%0D%0A4 kg⋅m/s
The momentum of an object is calculated by multiplying its mass by its velocity.
In this case, the object has a mass of 5 kg and a velocity of 20 m/s.
Therefore, the momentum of the object is:
Momentum = mass * velocity
Momentum = 5 kg * 20 m/s
Momentum = 100 kg⋅m/s
So, the correct response is: "100 kg⋅m/s".
Which of Newton’s laws of motion states that an object at rest stays at rest and an object in motion stays in motion with the same speed and the same direction unless acted upon by an unbalanced force?(1 point)%0D%0AResponses%0D%0A%0D%0ANewton’s fourth law of motion%0D%0ANewton ’ s fourth law of motion%0D%0A%0D%0ANewton’s first law of motion%0D%0ANewton ’ s first law of motion%0D%0A%0D%0ANewton’s second law of motion%0D%0ANewton ’ s second law of motion%0D%0A%0D%0ANewton’s third law of motion
The correct response is: "Newton’s first law of motion."
Which is always true in a closed system?
In a closed system, the total momentum is always conserved.
Which mathematical representation correctly identifies impulse? (1 point)%0D%0AResponses%0D%0A%0D%0Aimpulse=forcetime%0D%0Aimpulse%0D%0A=%0D%0Aforce%0D%0Atime%0D%0Aimpulse is equal to force over time%0D%0A%0D%0Aimpulse=velocitytime%0D%0Aimpulse%0D%0A=%0D%0Avelocity%0D%0Atime%0D%0Aimpulse is equal to velocity over time%0D%0A%0D%0Aimpulse=force×time%0D%0Aimpulse%0D%0A=%0D%0Aforce%0D%0A×%0D%0Atime%0D%0Aimpulse is equal to force times time%0D%0A%0D%0Aimpulse=acceleration×time
The correct mathematical representation that identifies impulse is:
impulse = force × time
This represents that impulse is equal to force times time.
In a closed system, a ball with a mass of 3 kg and a momentum of 24 kg·m/s collides into a ball with a mass of 1 kg that is originally at rest. Which statement describes the momentum of the balls and the total momentum?(1 point) Responses The momentum of each ball stays the same, and the total momentum stays the same. The momentum of each ball stays the same, and the total momentum stays the same. The momentum of each ball stays the same, and the total momentum changes. The momentum of each ball stays the same, and the total momentum changes. The momentum of each ball changes, and the total momentum changes. The momentum of each ball changes, and the total momentum changes. The momentum of each ball changes, and the total momentum stays the same. The momentum of each ball changes, and the total momentum stays the same. Skip to navigation page 11 of 11
In this scenario, the momentum of each ball changes, but the total momentum stays the same.
Initially, the first ball has a momentum of 24 kg·m/s, and the second ball is at rest with zero momentum.
After the collision, the first ball transfers some of its momentum to the second ball. Due to the conservation of momentum in a closed system, the total momentum before and after the collision must be the same. Thus, the momentum of each ball changes, but the total momentum remains constant.
The Moment of Impact Quick Check%0D%0A3 of 53 of 5 Items%0D%0A%0D%0AQuestion%0D%0AIn a closed system, three objects have the following momentums: 110 kg⋅m/s, −65 kg⋅m/s, and −100 kg⋅m/s. The objects collide and move together. What is the total momentum after the collision?(1 point)%0D%0AResponses%0D%0A%0D%0A55 kg⋅m/s%0D%0A55 kilograms times meters per second%0D%0A%0D%0A−55 kg⋅m/s%0D%0Anegative 55 kilograms times meters per second%0D%0A%0D%0A275 kg⋅m/s%0D%0A275 kilograms times meters per second%0D%0A%0D%0A−275 kg⋅m/s
To find the total momentum after the collision, we need to add up the momentums of all three objects.
The momentums given are:
110 kg⋅m/s
-65 kg⋅m/s
-100 kg⋅m/s
Adding them up:
110 kg⋅m/s + (-65 kg⋅m/s) + (-100 kg⋅m/s) = -55 kg⋅m/s
Therefore, the total momentum after the collision is -55 kg⋅m/s.
So, the correct response is: "−55 kg⋅m/s".
In a closed system, an object with a mass of 1.5 kg%0D%0A1.5%0D%0A %0D%0Akg%0D%0A collides with a second object. The two objects then move together at a velocity of 50 m/s. The total momentum of the system is 250 kg⋅m/s. What is the mass of the second object? (1 point)%0D%0AResponses%0D%0A%0D%0A1.5 kg%0D%0A1.5 kg%0D%0A%0D%0A3.0 kg%0D%0A3.0 kg%0D%0A%0D%0A3.5 kg%0D%0A3.5 kg%0D%0A%0D%0A5.0 kg
The total momentum of the system is the sum of momentums of both objects, given the formula:
Total momentum = mass of object 1 × velocity of object 1 + mass of object 2 × velocity of object 2
We know that the total momentum is 250 kg⋅m/s,
the mass of object 1 is 1.5 kg,
and the velocity of object 1 and 2 together is 50 m/s.
Let's assume the mass of the second object is x kg.
So the equation becomes:
250 kg⋅m/s = (1.5 kg) × (50 m/s) + x kg × (50 m/s)
Simplifying the equation:
250 kg⋅m/s = 75 kg⋅m/s + 50x kg⋅m/s
Rearranging the equation to isolate x:
50x kg⋅m/s = 250 kg⋅m/s - 75 kg⋅m/s
50x kg⋅m/s = 175 kg⋅m/s
x kg = 3.5 kg
Therefore, the mass of the second object is 3.5 kg.
So, the correct response is: "3.5 kg".
A cue stick has a mass of 0.5 kg. The cue stick hits a ball with a mass of 0.2 kg at a velocity of 2.5 m/s. What is the velocity of the ball after it is hit? (1 point)%0D%0AResponses%0D%0A%0D%0A6.3 m/s%0D%0A6.3 m/s%0D%0A%0D%0A3.6 m/s%0D%0A3.6 m/s%0D%0A%0D%0A8.3 m/s%0D%0A8.3 m/s%0D%0A%0D%0A2.5 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The initial momentum is given by:
Momentum = Mass × Velocity
Initial momentum = (0.5 kg) × (2.5 m/s) = 1.25 kg·m/s
Let's assume the velocity of the ball after it is hit is v m/s.
After the collision, the total momentum is still equal to 1.25 kg·m/s. Since the mass of the cue stick does not change and it is at rest after the collision, its momentum becomes 0 kg·m/s. Therefore, the momentum of the ball after the collision must be 1.25 kg·m/s.
Using the equation for momentum, we can solve for v:
Final momentum = Mass × Velocity
1.25 kg·m/s = (0.2 kg) × v
v = 1.25 kg·m/s / 0.2 kg
v = 6.25 m/s
Therefore, the velocity of the ball after it is hit is 6.25 m/s.
So, the correct response is: "6.3 m/s".
Enlightenment's Impact Quick Check%0D%0A1 of 51 of 5 Items%0D%0A%0D%0AQuestion%0D%0AWhich of the following statements best explains how Enlightenment thinkers challenged political authority?(1 point)%0D%0AResponses%0D%0A%0D%0AEnlightenment thinkers debated ways for one person or group to have complete power.%0D%0AEnlightenment thinkers debated ways for one person or group to have complete power.%0D%0A%0D%0AEnlightenment thinkers often debated ways to limit the power of the authority or government.%0D%0AEnlightenment thinkers often debated ways to limit the power of the authority or government.%0D%0A%0D%0AEnlightenment thinkers believed the monarchy should have absolute power. %0D%0AEnlightenment thinkers believed the monarchy should have absolute power. %0D%0A%0D%0AEnlightenment thinkers sided with the monarchy in disputes with the church.
The correct response is: "Enlightenment thinkers often debated ways to limit the power of the authority or government."
Enlightenment thinkers challenged political authority by advocating for limited or constitutional forms of government. They critiqued absolute monarchies and sought to establish checks and balances, separation of powers, and individual rights to limit the power of the ruling authorities.
What would an investigation into the cultural impacts of the Enlightenment conclude?(1 point)%0D%0AResponses%0D%0A%0D%0AIt would conclude that the Enlightenment increased the authority of the Catholic Church.%0D%0AIt would conclude that the Enlightenment increased the authority of the Catholic Church.%0D%0A%0D%0AIt would conclude that traditional ideas were favored over empirical observations.%0D%0AIt would conclude that traditional ideas were favored over empirical observations.%0D%0A%0D%0AIt would conclude that the power of monarchs was expanded. %0D%0AIt would conclude that the power of monarchs was expanded. %0D%0A%0D%0AIt would conclude that the Enlightenment led to the rise of new political structures and governments.%0D%0AIt would conclude that the Enlightenment led to the rise of new political structures and governments.
The correct response is: "It would conclude that the Enlightenment led to the rise of new political structures and governments."
An investigation into the cultural impacts of the Enlightenment would conclude that this intellectual movement played a pivotal role in promoting new ideas about governance, individual rights, and social structures. The Enlightenment challenged traditional ideas and advocated for reason, science, and progress. It led to the rise of new political systems and the establishment of democratic principles, such as the concept of popular sovereignty and the protection of individual liberties. The Enlightenment had a profound and lasting impact on cultural, political, and social developments during and after its time.