In the context of an experiment to prove the conservation of momentum, the students will multiply together mass and velocity before and after the collision. This is because momentum is defined as the product of mass and velocity (momentum = mass × velocity).
Some students conduct an experiment to prove conservation of momentum. They use two objects that collide. Measurements are taken before and after the collision. Which two quantities will the students multiply together before and after the collision?
Responses
mass and velocity
mass and acceleration
distance and time
velocity and time
9 answers
In a closed system, two moving bodies collide. There are no external forces acting on the system. How does the total momentum of the system before the collision compare with the total momentum of the system after the collision?
Responses
The total momentum after the collision is more than the total momentum before the collision.
The total momentum after the collision is the same as the total momentum before the collision.
The total momentum after the collision is less than the total momentum before the collision.
The total momentum after the collision is zero, while the total momentum before the collision is nonzero.
Responses
The total momentum after the collision is more than the total momentum before the collision.
The total momentum after the collision is the same as the total momentum before the collision.
The total momentum after the collision is less than the total momentum before the collision.
The total momentum after the collision is zero, while the total momentum before the collision is nonzero.
In a closed system with no external forces acting on it, the total momentum after the collision is the same as the total momentum before the collision. This statement reflects the principle of conservation of momentum.
As part of an experiment on momentum, a billiard ball with a mass of 0.180 kg travels 1.5 m in 0.5 s. What is the momentum of the ball?
Responses
0.06 kg⋅m/s
0.81 kg⋅m/s
0.54 kg⋅m/s
0.14 kg⋅m/s
Responses
0.06 kg⋅m/s
0.81 kg⋅m/s
0.54 kg⋅m/s
0.14 kg⋅m/s
To find the momentum of the billiard ball, we first need to calculate its velocity. Momentum (p) is calculated using the formula:
\[ p = m \times v \]
where:
- \( m \) is the mass,
- \( v \) is the velocity.
Step 1: Calculate the velocity.
Velocity is calculated as:
\[ v = \frac{\text{distance}}{\text{time}} = \frac{1.5 , \text{m}}{0.5 , \text{s}} = 3.0 , \text{m/s} \]
Step 2: Calculate the momentum.
Now we can calculate the momentum using the mass (\( m = 0.180 , \text{kg} \)) and the calculated velocity:
\[ p = 0.180 , \text{kg} \times 3.0 , \text{m/s} = 0.54 , \text{kg⋅m/s} \]
Thus, the momentum of the ball is 0.54 kg⋅m/s.
Two students perform an experiment with soccer balls. They kick two soccer balls so that they collide. They measure the total momentum of the two soccer balls before and after the collision. Which statement explains why the total momentum of the soccer balls before and after the collision may not be the same?
Responses
The soccer balls each have a different momentum after the collision than before the collision.
The system has external forces, such as friction and air resistance, acting on it.
The soccer balls exert forces on each other when they collide.
The system does not have any external forces.
Responses
The soccer balls each have a different momentum after the collision than before the collision.
The system has external forces, such as friction and air resistance, acting on it.
The soccer balls exert forces on each other when they collide.
The system does not have any external forces.
The correct response is: The system has external forces, such as friction and air resistance, acting on it.
In real-world scenarios, factors like friction from the ground and air resistance can influence the total momentum of the system, causing the total momentum before and after the collision to differ.
Two students in bumper cars want to prove conservation of momentum. They collide their bumper cars. The first bumper car has a mass of 120 kg
and was moving with a velocity of 4.0 m/s
before the collision and with a velocity of −2.0 m/s
after the collision. The second bumper car has a mass of 90 kg
and was moving at a velocity of −5.0 m/s
before the collision. To prove conservation of momentum, what must the velocity of the second bumper car be after the collision?
Responses
2.3 m/s
1.0 m/s
2.7 m/s
3.0 m/s
and was moving with a velocity of 4.0 m/s
before the collision and with a velocity of −2.0 m/s
after the collision. The second bumper car has a mass of 90 kg
and was moving at a velocity of −5.0 m/s
before the collision. To prove conservation of momentum, what must the velocity of the second bumper car be after the collision?
Responses
2.3 m/s
1.0 m/s
2.7 m/s
3.0 m/s
To prove conservation of momentum, we need to calculate the total momentum before and after the collision and set them equal to each other.
Step 1: Calculate the total momentum before the collision.
For the first bumper car:
- Mass \( m_1 = 120 , \text{kg} \)
- Velocity before the collision \( v_{1i} = 4.0 , \text{m/s} \)
Momentum of the first bumper car before the collision: \[ p_{1i} = m_1 \times v_{1i} = 120 , \text{kg} \times 4.0 , \text{m/s} = 480 , \text{kg⋅m/s} \]
For the second bumper car:
- Mass \( m_2 = 90 , \text{kg} \)
- Velocity before the collision \( v_{2i} = -5.0 , \text{m/s} \)
Momentum of the second bumper car before the collision: \[ p_{2i} = m_2 \times v_{2i} = 90 , \text{kg} \times (-5.0 , \text{m/s}) = -450 , \text{kg⋅m/s} \]
Total momentum before the collision: \[ p_{total , i} = p_{1i} + p_{2i} = 480 , \text{kg⋅m/s} + (-450 , \text{kg⋅m/s}) = 30 , \text{kg⋅m/s} \]
Step 2: Calculate the total momentum after the collision.
After the collision, the first bumper car's momentum: \[ p_{1f} = m_1 \times v_{1f} = 120 , \text{kg} \times (-2.0 , \text{m/s}) = -240 , \text{kg⋅m/s} \]
Let the velocity of the second bumper car after the collision be \( v_{2f} \).
The momentum of the second bumper car after the collision: \[ p_{2f} = m_2 \times v_{2f} = 90 , \text{kg} \times v_{2f} \]
Total momentum after the collision: \[ p_{total , f} = p_{1f} + p_{2f} = -240 , \text{kg⋅m/s} + (90 , \text{kg} \times v_{2f}) \]
Step 3: Set the total momentum before and after equal to each other: \[ p_{total , i} = p_{total , f} \] \[ 30 , \text{kg⋅m/s} = -240 , \text{kg⋅m/s} + 90 , \text{kg} \times v_{2f} \]
Step 4: Solve for \( v_{2f} \):
Add \( 240 , \text{kg⋅m/s} \) to both sides: \[ 30 , \text{kg⋅m/s} + 240 , \text{kg⋅m/s} = 90 , \text{kg} \times v_{2f} \] \[ 270 , \text{kg⋅m/s} = 90 , \text{kg} \times v_{2f} \]
Now divide both sides by \( 90 , \text{kg} \): \[ v_{2f} = \frac{270 , \text{kg⋅m/s}}{90 , \text{kg}} = 3.0 , \text{m/s} \]
Thus, the velocity of the second bumper car after the collision must be 3.0 m/s.