2021 AP Physics 1 Free Response #3 (First Administration)

Allen Tsao The STEM Coach
7 May 202109:47
EducationalLearning
32 Likes 10 Comments

TLDRThis video script discusses a physics problem from the 2021 AP Physics 1 exam involving a student pushing a disk on a frictionless surface with a constant force. The problem explores impulse, momentum, and the final velocities of both the disk and the student. It also includes scenarios where the disk collides with a block of different masses, estimating the velocity of the center of mass after the collision. The explanation uses conservation of momentum and impulse-momentum principles to derive equations and ratios, providing insights into the physics of the situation.

Takeaways
  • 📚 The script is a walkthrough of a physics problem from the 2021 AP Physics 1 exam.
  • 🧑‍🎓 A student with mass \( m_s \) uses a stick to apply a constant horizontal force \( F_h \) on a disk with mass \( m_d \) over time interval \( t_f \).
  • 🏋️‍♂️ The student and the disk are on a smooth surface with negligible friction.
  • 🔄 The impulse, which is the product of force and time, causes a change in momentum of the disk.
  • 📉 The final velocity of the disk \( v_d \) is found by dividing the impulse by the mass of the disk \( m_d \).
  • ⚖️ The ratio of the final velocities of the disk to the student \( v_d / v_s \) is derived to be \( m_s / m_d \).
  • 📈 The script discusses how to sketch graphs of the speeds of both the student and the disk as functions of time.
  • 💥 In a collision, if the disk's mass is much greater than the block's mass, the center of mass velocity \( v_{cm} \) is approximately equal to \( v_1 \), the initial velocity of the disk.
  • 🚫 Conversely, if the disk's mass is much less than the block's mass, the center of mass velocity \( v_{cm} \) is approximately zero.
  • 🔄 For a collision where neither object's mass is significantly greater, conservation of momentum is used to derive an equation for \( v_{cm} \).
  • 🔄 The script also checks if the equations derived for \( v_{cm} \) in different scenarios are consistent with the physical reasoning provided.
Q & A

  • What is the scenario described in the third question of the 2021 AP Physics 1 exam?

    -A student of mass ms is standing on a smooth surface and uses a stick to push a disk of mass md with a constant horizontal force fh over time from 0 to tf. The friction between the student's shoes and the surface is negligible.

  • What is the expression for the final speed of the disk relative to the surface?

    -The final speed of the disk (vd) can be determined using the impulse-momentum theorem, which states that the impulse (force times time, fh*t) is equal to the change in momentum (md*vd). Therefore, vd = (fh*t) / md.

  • How is the impulse defined in the context of this problem?

    -In this context, the impulse is defined as the product of the constant force (fh) and the time interval (t) over which the force is applied.

  • What is the relationship between the student's mass (ms) and the disk's mass (md) in determining the final speed of the student (vs)?

    -The student's final speed (vs) is determined by the impulse experienced by the student, which is the same as the impulse on the disk but in the opposite direction. Thus, vs = (fh*t) / ms. The ratio of the disk's final speed to the student's final speed is given by vs/vd = ms/md.

  • What is the significance of the assumption of negligible friction in this problem?

    -The assumption of negligible friction allows for the simplification of the problem by eliminating external forces that could affect the motion of the student and the disk, focusing solely on the force exerted by the student on the disk.

  • How can the ratio of the disk's final speed to the student's final speed be derived using conservation of momentum?

    -By considering the system consisting of the student and the disk, the total momentum before and after the interaction must be conserved. Since the disk exerts an equal and opposite impulse on the student, the ratio of their final speeds can be found by setting the initial momentum of the disk equal to the final momentum of the combined system.

  • What does the script suggest about the physical interpretation of the ratio of the student's mass to the disk's mass?

    -The script suggests that a larger student mass (ms) compared to the disk mass (md) would result in a smaller final speed for the student (vs), indicating that the student's motion would be less affected by the interaction.

  • How should the graph of the speeds of both the student and the disk as functions of time be sketched according to the script?

    -The graph should show the speeds (not velocities, hence ignoring direction) of both the student and the disk as linear functions of time, with the disk's speed increasing until tf and then remaining constant, while the student's speed would be proportional to the disk's but scaled by the ratio of their masses.

  • What happens when the disk, moving at a constant speed, collides head-on with a block of mass mb that is at rest on the surface?

    -The disk and the block collide and stick together, moving with a new velocity equal to the velocity of the center of mass of the combined system (vcm).

  • How is the velocity of the center of mass of the disk-block system estimated if the mass of the disk is much greater than that of the block?

    -If the disk's mass is much greater than the block's mass, the velocity of the center of mass (vcm) is approximately equal to the initial velocity of the disk (v1), as the impulse from the block on the disk is negligible.

  • What is the equation for the velocity of the center of mass of the disk-block system if neither object's mass is much greater than the other?

    -Using conservation of momentum, the equation for the velocity of the center of mass (vcm) after the collision is vcm = (md*v1 + mb*0) / (md + mb), where md is the mass of the disk, mb is the mass of the block, and v1 is the initial velocity of the disk.

Outlines
00:00
🚀 Impulse and Momentum in Physics Problem

The first paragraph discusses a physics problem from the 2021 AP Physics 1 exam involving a student exerting a constant horizontal force on a disk with negligible friction. The student's force over time is described as an impulse, which results in a change in the disk's momentum. The final speed of the disk is calculated using the impulse-momentum theorem, and the equation is derived as the impulse divided by the disk's mass. Additionally, the student's speed is derived using the same principles, and the ratio of the disk's speed to the student's speed is found to be the inverse of their masses. The paragraph concludes with a task to sketch graphs of the speeds of both the student and the disk as functions of time.

05:01
🎯 Collision Dynamics and Center of Mass Estimations

The second paragraph extends the physics scenario to include a collision between a moving disk and a stationary block. The discussion begins with the case where the disk's mass is significantly larger than the block's mass, leading to an estimate that the center of mass of the combined system will move at a speed close to the disk's initial speed due to the negligible impulse from the block. Conversely, if the disk's mass is much less than the block's, the center of mass velocity is estimated to be nearly zero. The paragraph then considers the case where neither mass is significantly larger, and a conservation of momentum equation is derived to calculate the velocity of the center of mass after the collision. The summary includes a comparison of the derived equation with the reasoning from the first scenario, confirming that the equations align with the physical expectations.

Mindmap
Keywords
💡Impulse
Impulse in physics is defined as the change in momentum of an object when a force is applied over a period of time. It is calculated as the product of force and the time interval during which the force is applied. In the video, impulse is used to explain how a constant force applied by a student over time 'tf' results in a change in the momentum of the disk, leading to its final velocity 'vd'. The script mentions 'impulse is force times the time', illustrating the concept by relating it to the student's action of pushing the disk.
💡Momentum
Momentum is the product of an object's mass and its velocity, representing the quantity of motion. It is a vector quantity, meaning it has both magnitude and direction. The video discusses momentum in the context of the change caused by the student's force on the disk, emphasizing that the final velocity of the disk is the result of the impulse (force times time) divided by the disk's mass 'md'. The script uses momentum to derive the final speed of the disk and to explain the ratio of velocities between the student and the disk.
💡Constant Force
A constant force is a force that does not change in magnitude or direction over time. In the video, the student applies a constant horizontal force 'fh' to the disk, which results in a linear change in the disk's velocity. The script describes this as the student exerting a force over a time interval from '0 to tf', which is fundamental to calculating the impulse and the resulting velocity of the disk.
💡Friction
Friction is the resistance that one surface or object encounters when moving over another. In the context of the video, the script mentions 'negligible friction', implying that the surfaces in contact (student's shoes and the smooth surface, and the disk and the surface) offer minimal resistance, allowing for the theoretical application of physics principles without the complicating factor of energy loss due to friction.
💡Velocity
Velocity is a vector quantity that represents the rate of change of an object's position with respect to time, including both speed and direction. The video script discusses the final velocity 'vd' of the disk and the velocity 'vs' of the student after applying the force. The script uses velocity to explain the ratio of the disk's speed to the student's speed and to analyze the outcomes of the collision between the disk and a block.
💡Ratio
A ratio is a mathematical expression that compares two quantities by division. In the video, the script derives an equation for the ratio of the final velocities of the disk 'vd' to the student 'vs', which is expressed in terms of their masses 'ms' and 'md'. The ratio is used to understand the relationship between the velocities of the two objects after the impulse is applied.
💡Conservation of Momentum
The conservation of momentum principle states that the total momentum of a closed system of objects remains constant if no external forces act upon it. The video script applies this principle to explain the outcomes of the collision between the disk and the block, stating that the momentum before the collision must equal the momentum after the collision, leading to an equation for the velocity of the center of mass 'vcm'.
💡Center of Mass
The center of mass is the point at which the mass of an object or system of objects can be considered to be concentrated for the purpose of analyzing motion. In the video, after the disk collides with the block, the script discusses the velocity of the center of mass of the combined system, 'vcm', as an estimate based on the relative masses of the disk and the block.
💡Collision
A collision occurs when two or more objects come into contact with each other, often resulting in changes in their motion. The video script describes a head-on collision between the disk and a block, where the disk's velocity before the collision and the combined velocity after the collision are analyzed using the conservation of momentum to estimate the new center of mass velocity 'vcm'.
💡Estimate
An estimate is an approximate calculation or judgment of the value, quantity, or extent of something. The video script uses estimates to determine the velocity of the center of mass 'vcm' in scenarios where the mass of the disk is much greater or much less than the mass of the block, providing a simplified understanding of the outcomes based on the relative masses.
Highlights

The problem involves a student using a stick to push a disk on a smooth surface with negligible friction.

A constant horizontal force is exerted on the disk over a time interval from 0 to tf.

The impulse exerted on the disk is equal to the force times the time (fh * t).

The final speed of the disk (vd) is determined by the impulse divided by the disk's mass (md).

The student's speed (vs) after applying the force is derived from the impulse divided by the student's mass (ms).

The ratio of the disk's final speed to the student's speed (vd/vs) is expressed in terms of their masses (ms/md).

Conservation of momentum or the concept of equal and opposite impulses can be used to derive the equation for vs.

The ratio vd/vs is inversely proportional to the ratio of the student's mass to the disk's mass.

The physical interpretation of the ratio is that a larger student mass results in a smaller speed change for the student.

The student and disk's speeds are to be sketched as functions of time, considering only positive values up to 2tf.

The disk's speed graph is expected to show a linear increase followed by a constant speed after tf.

The student's speed graph is influenced by the ratio of their masses and will be lower than the disk's.

The disk collides head-on with a block of mass mb, and the center of mass of the disk-block system moves with speed vcm.

If the disk's mass is much greater than the block's, the center of mass velocity is approximately equal to the disk's initial speed (v1).

If the disk's mass is much less than the block's, the center of mass velocity is approximately zero.

For a case where neither mass is significantly greater, conservation of momentum is used to derive the equation for vcm.

The derived equation for vcm in part c3 should agree with the reasoning for part c1 when md is much greater than mb.

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PhysicsImpulseMomentumForce AnalysisFrictionless SurfaceConstant ForceVelocity RatioCollision DynamicsCenter of MassMomentum Conservation