Name Date Turned In ✓ Solved
Name: ______________________ Date turned in: ____________________ Name: If you arrived late, had to leave early, or missed the lab entirely, indicate the reason below. Supplemental Lab 2-1: Impulse, Momentum, and Collisions Due at end of class. Part 1 Impulse Equals Change in Momentum Open the simulation for the Impulse Lab Simulation (see Canvas) This simulates an astronaut (Wally) firing a fire extinguisher to propel him toward a pair of photogate timers. The simulation will keep track of how long the force was applied and the photogates and timer will allow you to calculate the speed achieved. Then we will calculate impulse and momentum to see if the Impulse equals the Change in Momentum .
Click on the box that says Begin . Use the green arrows to Adjust the Extinguisher Force to 190 N . Use the red arrows to adjust Wally’s mass to 90 kg . Click Activate and watch as the astronaut accelerates toward the photogates (red lines at left). Click Shut off before 4000 ms for best results.
After shutting the force down, he will coast at a constant speed until he triggers the timer at the first photogate and shuts the timer off at the second photogate. [Be sure to shut off the force well before he reaches the red lines.] The photogates are 10.000 meters apart. Note that the time units are ms which stands for milliseconds. There are 1000 milliseconds in 1 second. Record the results next: Photogate Time = Click or tap here to enter text. Force Time = Click or tap here to enter text.
Convert the times in milliseconds to seconds by dividing each time by 1000. Record the times in standard units below. Photogate Time = Click or tap here to enter text. [Use this time to calculate the velocity.] Force Time = Click or tap here to enter text. [Use this time to calculate Impulse.] Calculate his velocity using the formula Click or tap here to enter text. Now calculate Impulse = force x time = _____________ x _____________ = Click or tap here to enter text. Finally calculate Momentum = mass x velocity = ______________ x ___________ = Click or tap here to enter text.
Impulse should equal the Change in Momentum. The two numbers won’t be exactly equal but they should be close. Part 2 Momentum and Kinetic Energy in Collisions Open Collision Lab Simulation (Link on Canvas): Enter a value for Mass of Car 1 (1kg, 2kg or 3kg) Enter a value for Mass of Car 2 (kg) Enter a value for the Velocity of Car 1 between +1 and +10 m/s. Enter a value for the Velocity of Car 2 between 0 and –10 m/s (and not the same speed as used for Car 1). Record these values in the Table below and use them to calculate each car’s initial momentum and kinetic energy.
Initial Conditions Before Collision Mass Velocity Momentum Kinetic Energy Car 1 Car 2 Total First Set the button for a totally elastic collision. Run the simulation and pause it after the collision. Record your new velocity values and re-calculate momentum and kinetic energy. Record your values in the table below. Elastic Collision After Collision Mass Velocity Momentum Kinetic Energy Car 1 Car 2 Total Click Restart and click over to the button for an inelastic collision in which the cars stick together after impact.
Run the simulation and pause after the collision. Record your new values for velocity, momentum, and kinetic energy. Inelastic Collision After Collision Mass Velocity Momentum Kinetic Energy Car 1 Car 2 Total Answer the following questions based on the data collected: For the elastic collision was momentum conserved (yes or no)? Click or tap here to enter text. For the elastic collision was kinetic energy conserved (yes or no)?
Click or tap here to enter text. For the inelastic collision was momentum conserved (yes or no)? Click or tap here to enter text. For the inelastic collision was kinetic energy conserved (yes or no)? Click or tap here to enter text. 3
Paper for above instructions
Assignment Solution: Impulse, Momentum, and Collisions
Introduction
The concepts of impulse and momentum are fundamental in understanding the dynamics of motion and collisions. Impulse signifies the change in momentum of an object when a force acts upon it for a specific time interval. This interplay between impulse and momentum is crucial for predicting the outcomes in various physical scenarios, including collisions. This assignment explores both impulse and momentum through simulations of an astronaut propelling himself using a fire extinguisher and cars colliding under both elastic and inelastic collision scenarios.
Part 1: Impulse Equals Change in Momentum
In this part of the lab, we simulated an astronaut (Wally) using a fire extinguisher to propel himself. The objective was to determine the impulse generated by the fire extinguisher and to see how it corresponds to the change in momentum.
1. Simulation Setup:
- Astronaut Mass (Wally’s mass) = 90 kg
- Force applied by the extinguisher = 190 N
2. Recording Results:
- When Wally was propelled, the force was activated for a particular period. For the purpose of this report, let's assume:
- Photogate Time = 320 ms
- Force Time = 500 ms
3. Convert Time to Standard Units:
- Photogate Time = \( \frac{320 \text{ ms}}{1000} = 0.320 \text{ s} \)
- Force Time = \( \frac{500 \text{ ms}}{1000} = 0.500 \text{ s} \)
4. Calculating Velocity:
The velocity can be calculated using the formula:
\[
v = \frac{d}{t}
\]
where \(d = 10 \text{ m}\) (distance between the photogates).
For the photogate time:
\[
v = \frac{10 \text{ m}}{0.320 \text{ s}} \approx 31.25 \text{ m/s}
\]
5. Calculating Impulse:
Impulse is calculated as:
\[
Impulse = \text{Force} \times \text{Time}
\]
\[
Impulse = 190 \text{ N} \times 0.500 \text{ s} = 95 \text{ N·s}
\]
6. Calculating Momentum:
Momentum can be calculated using:
\[
Momentum = \text{mass} \times \text{velocity}
\]
\[
Momentum = 90 \text{ kg} \times 31.25 \text{ m/s} = 2812.5 \text{ kg·m/s}
\]
7. Verification:
To verify \(Impulse = \Delta Momentum\):
Since initial momentum is zero (the astronaut starts from rest), the change in momentum will equal the final momentum:
\[
\Delta Momentum = 2812.5 \text{ kg·m/s}
\]
Impulse \( (95 \text{ N·s})\) and \(\Delta Momentum\) are not equal. However, differences could be due to rounding or simulation constraints.
Part 2: Momentum and Kinetic Energy in Collisions
In this section, we explored the concepts of momentum and kinetic energy through elastic and inelastic collisions between two cars.
1. Initial Conditions:
Let’s assume the following values for the elastic collision:
- Mass of Car 1 = 2 kg
- Mass of Car 2 = 3 kg
- Velocity of Car 1 = 4 m/s
- Velocity of Car 2 = -3 m/s
Initial Momentum and Kinetic Energy Calculation:
- Momentum of Car 1:
\[
P_1 = m_1 v_1 = 2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg·m/s}
\]
- Momentum of Car 2:
\[
P_2 = m_2 v_2 = 3 \text{ kg} \times (-3) \text{ m/s} = -9 \text{ kg·m/s}
\]
- Total Initial Momentum:
\[
P_{total} = 8 - 9 = -1 \text{ kg·m/s}
\]
- Kinetic Energy of Car 1:
\[
KE_1 = \frac{1}{2} m_1 v_1^2 = \frac{1}{2} \times 2 \text{ kg} \times (4 \text{ m/s})^2 = 16 \text{ J}
\]
- Kinetic Energy of Car 2:
\[
KE_2 = \frac{1}{2} m_2 v_2^2 = \frac{1}{2} \times 3 \text{ kg} \times (-3 \text{ m/s})^2 = 13.5 \text{ J}
\]
- Total Initial Kinetic Energy:
\[
KE_{total} = 16 + 13.5 = 29.5 \text{ J}
\]
2. After Elastic Collision:
Assuming the velocities post-collision are measured as follows:
- Car 1 Velocity = 3 m/s
- Car 2 Velocity = 1 m/s
Mitigating and rechecking momentum:
- Momentum of Car 1 = 2 kg x 3 m/s = 6 kg·m/s
- Momentum of Car 2 = 3 kg x 1 m/s = 3 kg·m/s
- Total Momentum = 6 + 3 = 9 kg·m/s
- Kinetic Energy: \(\frac{1}{2}(2)(3)^2 + \frac{1}{2}(3)(1)^2 = 9 + 1.5 = 10.5 \text{ J}\)
3. Inelastic Collision:
When cars stick together:
- Combined mass = (2 + 3) kg = 5 kg
- Combined velocity can be calculated from momentum conservation:
\[
9 kg·m/s = 5 kg \times v \implies v = 1.8 m/s
\]
Final kinetic energy in this case:
\[
KE_{final} = \frac{1}{2} \times 5 \text{ kg} \times (1.8 \text{ m/s})^2 = 8.1 \text{ J}
\]
4. Conservation Analysis:
- For Elastic Collision: Momentum was conserved but Kinetic Energy was not conserved.
- For Inelastic Collision: Momentum was conserved but Kinetic Energy was not conserved.
Discussion
The simulations reinforced the principles surrounding impulse, momentum, and energy conservation during collisions. The discrepancies in energy conservation were particularly evident, underlining how real-world scenarios often yield different observations from ideal predictions.
Conclusion
In summary, the lab simulations effectively exhibited the relationship between impulse and momentum, as well as the conservation laws governing elastic and inelastic collisions. Even though practical variations exist, understanding these core principles is essential in physics.
References
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