AP Physics 1 Kinematics Free Response 10

Allen Tsao The STEM Coach
16 Nov 201807:59
EducationalLearning
32 Likes 10 Comments

TLDRIn this physics tutorial, Alan from Bothell STEM explores a kinematics problem inspired by the Star Trek reboot. He calculates the coefficient of kinetic friction between young Kirk and the ground, using the car's trajectory and distance to solve for initial velocity and acceleration, ultimately determining the friction coefficient as 0.9.

Takeaways
  • πŸš— The video discusses a physics problem based on a scene from the Star Trek reboot movie where young Kirk jumps out of a speeding car.
  • πŸƒ The car was traveling at an unknown velocity \( V \) when Kirk jumped out, and this velocity is a key variable in solving the problem.
  • πŸš— Kirk slides along the ground for a distance \( D = 5 \) meters before stopping at the edge of a cliff.
  • πŸ”οΈ The car flies off the cliff after falling a height of 50 meters and lands 30 meters from the bottom of the cliff.
  • πŸ” The problem requires determining the coefficient of kinetic friction between Kirk and the ground.
  • 🧠 The solution involves using kinematic equations to find the initial velocity \( V_0 \) of the car before Kirk jumped out.
  • πŸ“š The horizontal displacement equation \( D = V_0 T + \frac{1}{2} a t^2 \) is used, with \( a = 0 \) since there is no horizontal acceleration.
  • ⏱️ The time \( T \) in the air is determined by the vertical displacement equation \( H = \frac{1}{2} g T^2 \), where \( g \) is the acceleration due to gravity.
  • πŸ”’ The initial velocity \( V_0 \) is calculated as \( D \sqrt{\frac{g}{2H}} \), using the distance \( D \), gravitational acceleration \( g \), and height \( H \).
  • πŸ›‘ Kirk's sliding distance and the frictional force are used to derive the equation for the acceleration due to friction.
  • πŸ“‰ The coefficient of friction \( \mu_k \) is found by dividing the acceleration due to friction by \( g \), resulting in \( \mu_k = 0.9 \).
Q & A
  • What is the topic of the video?

    -The video is about solving AP Physics kinematics problems, specifically one involving a scene from the Star Trek reboot movie.

  • What is the scenario described in the video?

    -The scenario involves young Kirk dropping out of a speeding Corvette, sliding along the ground, and stopping at the edge of a cliff while the car flies off the cliff.

  • What is the distance Kirk slides before stopping?

    -Kirk slides a distance of 5 meters before stopping at the edge of the cliff.

  • What is the height from which the car falls off the cliff?

    -The car falls off the cliff from a height of 50 meters.

  • How far does the car hit the ground from the bottom of the cliff?

    -The car hits the ground 30 meters from the bottom of the cliff.

  • What is the initial velocity of the car (V naught)?

    -The initial velocity of the car, V naught, is not known but can be determined from the problem.

  • What assumption is made about the car's speed after Kirk drops out?

    -The assumption is that the car did not slow down after Kirk dropped out of it.

  • What is the equation used to find the initial velocity (V naught)?

    -The equation used to find the initial velocity is V naught = D / sqrt(2H/g), where D is the distance Kirk slides, H is the height the car falls, and g is the acceleration due to gravity.

  • What is the equation used to find the acceleration due to friction?

    -The equation used to find the acceleration due to friction is a = - (d^2 * g) / (2 * H * D), where d is the distance Kirk slides, H is the height the car falls, and g is the acceleration due to gravity.

  • What is the coefficient of kinetic friction between Kirk and the ground?

    -The coefficient of kinetic friction between Kirk and the ground is determined to be 0.9.

  • What advice does the video give regarding calculations?

    -The video advises not to put numbers in the very end of the calculations, suggesting a focus on understanding the process rather than just the final numerical answer.

Outlines
00:00
πŸš— Physics Kinematics Problem from Star Trek Scene

In this paragraph, Alan introduces a physics kinematics problem inspired by a scene from the Star Trek reboot movie. The problem involves calculating the coefficient of kinetic friction between young Kirk and the ground after he jumps out of a speeding Corvette and slides to a stop at the edge of a cliff. Alan encourages viewers to attempt the problem before revealing the solution. The scenario describes Kirk's uncle's car being chased by a robot cop, leading to Kirk's daring escape and subsequent slide. The problem requires determining the initial velocity (V naught) of the car, which can be deduced from the car's flight path over the cliff and the distance it travels after impact. Alan outlines the physics equations and assumptions involved in solving for V naught, emphasizing the importance of considering both horizontal and vertical motion.

05:01
πŸ“š Solving for Coefficient of Friction Using Kinematic Equations

Alan continues the physics problem by focusing on the calculation of the coefficient of kinetic friction (mu K) between young Kirk and the ground. He uses the previously determined initial velocity of the car to find the acceleration Kirk experienced while sliding. By rearranging the kinematic equation for final velocity (VF squared = V naught squared + 2aΞ”x), Alan isolates the acceleration due to friction. He then relates this acceleration to the frictional force, which is the net force acting on Kirk, and equates it to the product of the coefficient of friction and the normal force (mu K = a/G). After substituting the known values and performing the calculation, Alan concludes that the coefficient of friction is 0.9. He wraps up the explanation by inviting viewers to engage with the content through comments, likes, and subscriptions, and mentions offering free homework help on platforms like Twitch and Discord.

Mindmap
Keywords
πŸ’‘AP Physics
AP Physics refers to a high school course that prepares students for the Advanced Placement exam in Physics. In the video, it sets the context for the type of physics problems being discussed, specifically kinematics problems. The script mentions 'ap physics kinematics problems,' indicating that the video is educational and focused on helping students understand the principles of motion.
πŸ’‘Kinematics
Kinematics is a branch of physics that deals with the motion of objects without considering the forces that cause the motion. In the script, the video focuses on 'ap physics kinematics problems,' which involves analyzing the motion of objects like the car and young Kirk in the Star Trek scenario, using principles such as displacement, velocity, and acceleration.
πŸ’‘Star Trek
Star Trek is a popular science fiction franchise that serves as the backdrop for the physics problem in the video. The script uses a scene from the Star Trek reboot movie where 'young Kirk drops out of a Corvette,' to introduce a real-world scenario that can be analyzed using kinematics. This makes the physics concepts more relatable and engaging.
πŸ’‘Velocity
Velocity is a measure of an object's speed in a specific direction. The script mentions 'velocity V' in the context of the car's speed and young Kirk's jump from the car. It is a crucial parameter in the kinematics equations used to solve for the initial velocity (V naught) and to analyze the motion in both horizontal and vertical directions.
πŸ’‘Displacement
Displacement is the change in an object's position from its initial point to its final point. In the video script, 'D equals 5 meters' refers to the horizontal displacement of young Kirk as he slides along the ground before stopping at the edge of the cliff. Displacement is used to calculate the initial velocity and to understand the motion in the x-direction.
πŸ’‘Acceleration
Acceleration is the rate of change of velocity of an object. The script discusses 'frictional acceleration' experienced by young Kirk as he slides along the ground. It is a key factor in determining the deceleration due to friction, which helps in calculating the coefficient of kinetic friction between Kirk and the ground.
πŸ’‘Coefficient of Kinetic Friction
The coefficient of kinetic friction is a dimensionless scalar that represents the ratio of the force of friction between two bodies to the force pressing them together. In the script, the problem involves finding this coefficient by analyzing the motion of young Kirk sliding to a stop. It is calculated using the formula ΞΌ_k = a / g, where a is the acceleration due to friction and g is the acceleration due to gravity.
πŸ’‘Initial Velocity
Initial velocity, often denoted as V naught, is the velocity of an object at the beginning of its motion. The script aims to determine the 'initial velocity so I know that this is 30,' referring to the car's speed at the cliff's edge. This is crucial for understanding how fast Kirk was moving when he jumped from the car.
πŸ’‘Free Fall
Free fall is the motion of an object under the influence of gravity alone, without any other forces acting on it. The script mentions the car 'falling a height of 50 meters,' which is an example of free fall. The time it takes for the car to fall and the distance it travels upon impact are analyzed to determine the car's initial velocity.
πŸ’‘Frictional Force
Frictional force is the force that opposes the relative motion or tendency of such motion between two surfaces in contact. In the script, the problem involves calculating the frictional force acting on young Kirk as he slides along the ground, which is crucial for determining the coefficient of kinetic friction. The frictional force is related to the normal force and the coefficient of friction.
Highlights

Alan introduces an AP Physics kinematics problem related to the Star Trek reboot movie.

Young Kirk drops out of a speeding Corvette, slides along the ground, and stops at the edge of a cliff.

The car flies off the cliff after falling a height of 50 meters.

The car hits the ground 30 meters from the bottom of the cliff.

The problem involves finding the coefficient of kinetic friction between Young Kirk and the ground.

It is assumed that the car did not slow down after Kirk dropped out.

Alan recommends not putting numbers in the very end of the calculations.

The initial velocity (V naught) is not known but can be determined.

Alan uses the equation D = V naught * T to solve for V naught.

The time T in the air is determined using the vertical displacement H.

The initial velocity V naught is calculated as D * sqrt(G) / (2 * H).

Kirk slides a distance D meters before stopping.

The final velocity (VF) is zero as Kirk stops at the edge of the cliff.

The equation VF^2 = V naught^2 + 2 * a * delta X is used to solve for acceleration a.

The acceleration a is calculated as -1/2 * D^2 * G / (2 * H).

The frictional force is the net force on Kirk, which is mass times acceleration.

The coefficient of friction (mu K) is calculated as a / G.

The final coefficient of friction is found to be 0.9.

Alan offers free homework help on Twitch and Discord.

Transcripts
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