The chart show the masses and velocities of two colliding objects that stick together after a collision.
According to the law of conservation of momentum, what is the momentum of the object after the collision?
4,500 g · m/s
1,750 g · m/s
1,500 kg · m/s
3,000 kg · m/s
The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision.
In this case, the momentum of the objects before the collision is (mass1 * velocity1) + (mass2 * velocity2), and after the collision, when the objects stick together, the momentum is given by (mass1 + mass2) * velocity_after.
Looking at the chart, the masses of the two objects add up to 2,000 grams or 2 kilograms, and the velocity after the collision is given as 1.5 m/s.
Therefore, the momentum of the objects after the collision is (2 kg) * (1.5 m/s) = 3 kg · m/s or 3,000 kg · m/s.
To calculate the momentum of the objects after the collision, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The formula for momentum is:
Momentum = mass × velocity
Let's calculate the momentum of each object before the collision:
Object 1:
Mass = 2,000 g = 2 kg
Velocity = 3 m/s
Momentum of object 1 before collision = 2 kg × 3 m/s = 6 kg·m/s
Object 2:
Mass = 1,500 g = 1.5 kg
Velocity = 0 m/s (since it is at rest)
Momentum of object 2 before collision = 1.5 kg × 0 m/s = 0 kg·m/s
The total momentum of the system before the collision is the sum of the momenta of object 1 and object 2:
Total momentum before collision = 6 kg·m/s + 0 kg·m/s = 6 kg·m/s
Since the objects stick together after the collision, their masses will combine:
Total mass after collision = 2 kg + 1.5 kg = 3.5 kg
Now, we can calculate the momentum of the combined objects after the collision.
Total momentum after collision = Total mass after collision × velocity after collision
The velocity after the collision is not given in the question, so we cannot determine the exact momentum value. Please provide the velocity after the collision to calculate the momentum accurately.
To determine the momentum of the objects after the collision, we need to calculate the total momentum before the collision and use the law of conservation of momentum. The law states that the total momentum of a closed system remains constant before and after a collision.
To calculate the total momentum before the collision, we multiply the mass of each object by its velocity and add them together.
Ptotal = m1 * v1 + m2 * v2
We are given the masses and velocities of the two colliding objects, but the values are in different units: grams (g) and kilograms (kg). We need to convert the units to be consistent.
Let's convert the masses first:
Mass1 = 4,500 g = 4.5 kg
Mass2 = 1,750 g = 1.75 kg
Next, let's calculate the total momentum using the converted masses:
Ptotal = (Mass1 * v1) + (Mass2 * v2)
= (4.5 kg * v1) + (1.75 kg * v2)
From the provided options, we can calculate the total momentum using each of them and compare it with the equation above to find the correct answer.
Option 1: Ptotal = 4,500 g · m/s = (4.5 kg * v1) + (1.75 kg * v2)
Option 2: Ptotal = 1,750 g · m/s = (4.5 kg * v1) + (1.75 kg * v2)
Option 3: Ptotal = 1,500 kg · m/s = (4.5 kg * v1) + (1.75 kg * v2)
Option 4: Ptotal = 3,000 kg · m/s = (4.5 kg * v1) + (1.75 kg * v2)
By substituting all the options into the equation, we can determine which one satisfies the equation for the given masses and velocities.
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UNIT TEST.
Xander reached a final velocity of 4.5 m/s for 3.5 seconds. Finley reached a final velocity of 3.6 m/s for 4.2 seconds. Max reached a final velocity of 7.3 m/s for 1.2 seconds. They all started at the same location from rest.
Which lists them from least to most acceleration?
Max Finley Xander
Max Xander Finley
Xander Finley Max
Finley Xander Max
Acceleration is given by the equation:
Acceleration = (Final velocity - Initial velocity) / Time
Let's calculate the acceleration for each person:
Xander:
Initial velocity = 0 m/s (since he started from rest)
Final velocity = 4.5 m/s
Time = 3.5 seconds
Acceleration of Xander = (4.5 m/s - 0 m/s) / 3.5 seconds = 1.29 m/s²
Finley:
Initial velocity = 0 m/s (since he started from rest)
Final velocity = 3.6 m/s
Time = 4.2 seconds
Acceleration of Finley = (3.6 m/s - 0 m/s) / 4.2 seconds = 0.86 m/s²
Max:
Initial velocity = 0 m/s (since he started from rest)
Final velocity = 7.3 m/s
Time = 1.2 seconds
Acceleration of Max = (7.3 m/s - 0 m/s) / 1.2 seconds = 6.08 m/s²
Arranging them in order from least to most acceleration:
Finley (0.86 m/s²) < Xander (1.29 m/s²) < Max (6.08 m/s²)
So, the correct answer is: Finley Xander Max.
Two objects collide and bounce apart. Assuming no outside forces act on the system, which best describes the total momentum after the collision?
It is always greater than it was before the collision.
It is often greater than it was before the collision.
It is always the same as it was before the collision.
It is often the same as it was before the collision.
According to the law of conservation of momentum, the total momentum of a system before a collision is equal to the total momentum after the collision if no external forces are present. Therefore, the correct answer is:
It is always the same as it was before the collision.
The table represents the speed of a car in a northern direction over several seconds.
A 2-column table with 5 rows. The first column labeled Column 1 has entries 0, 2, 4, 6, 8, 10. The second column labeled Column 2 has entries 5, 10, 15, 20, 25, 30.
Column 1 would be on the x-axis, and Column 2 would be on the y-axis. Which best lists the titles of each column?
Column 1 should be titled “Time,” and Column 2 should be titled “Velocity.”
Column 1 should be titled “Velocity,” and Column 2 should be titled “Time.”
Column 1 should be titled “Time,” and Column 2 should be titled “Acceleration.”
Column 1 should be titled “Acceleration,” and Column 2 should be titled “Time.”
From the given information, it is clear that the first column represents time in seconds, and the second column represents velocity in a northern direction. Therefore, the correct titles for each column would be:
Column 1 should be titled “Time,” and Column 2 should be titled “Velocity.”
Engineers are trying to improve a race car. Their goal is to increase the acceleration of the car using the same engine. Which change shows the best application of Newton’s laws of motion to achieve this goal?
increasing the inertia of the car
decreasing the reaction force
increasing the action force
decreasing the mass of the car
To increase the acceleration of the race car using the same engine, the best application of Newton's laws of motion would be to decrease the mass of the car.
According to Newton's second law of motion (F = ma), the acceleration of an object is directly proportional to the force applied and inversely proportional to the mass of the object. By decreasing the mass of the car while keeping the same engine, the same force applied will result in a greater acceleration.
Which describes an object’s speed when free falling in a vacuum?
The object accelerates until it reaches its terminal velocity.
The object falls at a constant speed because only one force acts on it.
The object falls faster and faster until it strikes the ground.
The object speeds up and then stops when air resistance equals gravity.
In a vacuum, an object's speed when free falling would be described as follows:
The object accelerates until it reaches its terminal velocity.
In a vacuum, there is no air resistance or any other force to slow down the object's acceleration. Therefore, the object will continue to increase in speed until it reaches a point where its weight is balanced by the force of air resistance, resulting in a constant velocity known as terminal velocity.
Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same. How do Newton’s laws explain why the scientists could expect this to happen?
The total force stays the same, but the action force is increasing as the reaction decreases.
The mass of the rocket decreases as fuel is burned, so the acceleration increases.
The inertia of the rocket increases, which reduces the force needed to change its speed.
The reaction force is increasing as fuel is burned, which causes a greater acceleration.
Newton's laws of motion can explain why the acceleration of the rocket is increasing while the force exerted by its engines stays the same as it gets higher.
The correct explanation is:
The mass of the rocket decreases as fuel is burned, so the acceleration increases.
According to Newton's second law of motion (F = ma), the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. As the rocket climbs higher, it burns fuel, which decreases its mass. Since the force exerted by the engines remains constant, the decrease in mass leads to an increase in acceleration. This is because the same force applied to a smaller mass results in a greater acceleration.
What is determined by calculating the slope of the position vs time graph?
position
velocity
distance
displacement
The slope of a position vs. time graph determines the velocity of an object.
Velocity is defined as the rate of change of position with respect to time. Therefore, calculating the slope of a position vs. time graph gives you the ratio of the change in position to the change in time, which corresponds to the average velocity of the object during that time interval.
A factory employee spends two hours putting together a car part. A machine can do the same job in thirty minutes.
Which statement best describes the time-effectiveness of this scenario?
The employee is four times as time-effective as the machine.
The machine is half as time-effective as the employee.
The employee is half as time-effective as the machine.
The machine is four times as time-effective as the employee.
To determine the time-effectiveness, we need to compare the time it takes for the employee to complete the task with the time it takes for the machine to complete the same task.
The employee takes two hours, which is equivalent to 120 minutes, to complete the job.
The machine takes thirty minutes to complete the job.
To calculate the time-effectiveness, we divide the time taken by the employee by the time taken by the machine.
Time-effectiveness = Time taken by the employee / Time taken by the machine
Time-effectiveness = 120 minutes / 30 minutes
= 4
Hence, the correct statement is:
The machine is four times as time-effective as the employee.
Rachel wants to develop a lamp that will work using a remote control. Which statement best describes the process she should use?
She should use scientific investigation because she will need to analyze the results.
She should use technological design because she will need to design an experiment.
She should use scientific investigation because she will need to communicate her findings.
She should use technological design because she will need to build a prototype.
Rachel should use technological design because she will need to design and build a prototype for the lamp that works using a remote control.
Technological design involves applying scientific and engineering principles to create practical solutions to problems, such as designing and building products or systems. In this case, Rachel wants to develop a lamp that functions with a remote control, which requires designing and building a prototype that incorporates the necessary technology and components. Therefore, the most suitable approach for Rachel is technological design.
What must be included when describing the displacement of an object?
measurement and direction
direction and speed
total distance and position
speed and total distance
When describing the displacement of an object, it is important to include the measurement and direction.
Displacement refers to the change in position of an object from its initial position to its final position. It is a vector quantity, meaning it not only includes the magnitude (or measurement) of the change but also the direction of the change.
For example, if an object moves 10 meters to the east, the displacement would be described as "10 meters east." The 10 meters represents the measurement or magnitude of the change, and the "east" represents the direction in which the change occurred.
Kai was 200 meters north of the library when he remembered he had to return some books to the library. It took him 200 seconds to do the round trip.
Which best describes Kai’s roundtrip?
His speed was 1 m/s, and his velocity was 0.
His speed was 2 m/s, and his velocity was 0.
His speed was 1 m/s, and his velocity was 1 m/s north.
His speed was 2 m/s, and his velocity was 2 m/s south.
To determine the best description of Kai's roundtrip, we need to calculate his speed and velocity.
Speed is defined as the distance traveled per unit of time. In this case, Kai traveled a total distance of 400 meters (200 meters going north and 200 meters returning). The total time taken was 200 seconds.
Speed = Total distance / Total time
Speed = 400 meters / 200 seconds
Speed = 2 m/s
Velocity, on the other hand, is the speed of an object in a given direction. Since Kai started 200 meters north of the library and returned to the same position, the displacement of his round trip is 0 meters.
Therefore, the correct description for Kai's roundtrip is:
His speed was 2 m/s, and his velocity was 0.
What kind of acceleration occurs when an object speeds up?
positive
negative
neutral
zero
When an object speeds up, the type of acceleration that occurs is positive.
Acceleration is defined as the rate of change of velocity. When an object speeds up, it means that its velocity is increasing, which results in a positive acceleration. Positive acceleration indicates that the object is moving in the positive direction or accelerating in the same direction as its velocity.
Sayid made a chart listing data of two colliding objects.
A 5-column table titled Collision: Two Objects Stick Together with 2 rows in the first 3 columns and 1 row in the last 2 columns. The first column labeled Object has entries X, Y. The second column labeled Mass before Collision (kilograms) has entries 300, 100. The third column labeled Velocity before Collision (meters per second) has entries 10, negative 6. The fourth column labeled Mass after Collision (kilograms) has entry 400. The fifth column labeled Velocity after Collision (meters per second) has entry ?.
According to the law of conservation of momentum, what is the missing value in the chart?
4
6
10
16
According to the law of conservation of momentum, the total momentum before a collision is equal to the total momentum after the collision.
To calculate the momentum before the collision, we multiply the mass of each object by its velocity and sum them up.
For Object X before the collision:
Momentum_X_before = Mass_X * Velocity_X_before
= 300 kg * 10 m/s
= 3000 kg·m/s
For Object Y before the collision:
Momentum_Y_before = Mass_Y * Velocity_Y_before
= 100 kg * (-6 m/s)
= - 600 kg·m/s (negative sign indicates opposite direction)
The total momentum before the collision is the sum of Momentums_X_before and Momentums_Y_before:
Total momentum before collision = Momentum_X_before + Momentum_Y_before
= 3000 kg·m/s + (-600 kg·m/s)
= 2400 kg·m/s
According to the law of conservation of momentum, this total momentum before the collision must be equal to the total momentum after the collision.
Total momentum after collision = Total_mass_after_collision * Velocity_after_collision
Total_mass_after_collision = Mass_X_after + Mass_Y_after
= 400 kg
Using the equation: 2400 kg·m/s = 400 kg * Velocity_after_collision
We can solve for Velocity_after_collision:
Velocity_after_collision = 2400 kg·m/s / 400 kg = 6 m/s
Therefore, the missing value in the chart, Velocity after Collision, is 6.
What is the first stage of both technological design and scientific investigation?
communicate the findings
evaluate the product
identify a problem
conduct background research
The first stage of both technological design and scientific investigation is to identify a problem
Levi and Clara are trying to move a very heavy box. Levi is pushing the box with a force of 30 N, and Clara is pulling the box with a force of 50 N. The box exerts a frictional force of 65 N.
Which best explains the forces?
There is a net force of 15 N against them and they cannot move the box.
There is a net force of 15 N allowing Levi and Clara to move the box.
There is a net force of 65 N against them and they cannot move the box.
There is a net force of 80 N allowing Levi and Clara to move the box.
I DONT LIKE IT WHEN U DONT ANSWER ANYMORE copy n paste this:
Levi and Clara are trying to move a very heavy box. Levi is pushing the box with a force of 30 N, and Clara is pulling the box with a force of 50 N. The box exerts a frictional force of 65 N.
Which best explains the forces?
There is a net force of 15 N against them and they cannot move the box.
There is a net force of 15 N allowing Levi and Clara to move the box.
There is a net force of 65 N against them and they cannot move the box.
There is a net force of 80 N allowing Levi and Clara to move the box.
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