4 min readβ’november 2, 2020

Peter Apps

The **Paragraph-Length Response** is one of the 5 FRQs that appear on the AP Physics 1 Exam. This particular question is usually worth 7 points (out of a total of 45) and is suggested to take around 13 minutes to complete.

From CollegeBoard:

AP Physics students are asked to give a paragraph-length response so that they may demonstrate
their ability to communicate their understanding of a physical situation in a reasoned, expository
analysis. A studentβs response should be a **coherent, organized, and sequential description** of the
analysis of a situation. The response should **argue from evidence, cite physical principles, and**

So we need to have a logical, organized argument that describes a situation from given evidence and basic physics principles. To do that I recommend using the following Claim, Evidence, Reasoning (CER) format:

With this format in mind, let's apply it to a sample problem.

- Both objects are in freefall (the only force acting on them is the force of gravity)
- Vertical and Horizontal motion are independent of each other
- Possible useful equation(s) from the reference table (Kinematics & Forces):

- Same Forces & Masses --> Same Vertical Acceleration
- Same Height, Starting Vertical Velocity, and Vertical Acceleration --> Same time to fall
- Rewriting equation #2 and solving for time might be useful too

The spheres will hit the ground at the same time because their vertical motion is independent of their horizontal motion. The time to fall can be calculated using y = yo + voyt + 1/2at^2. The spheres both start with the same vertical initial velocities, acceleration (g), and distance above the ground. This lets us simplify the equation to t = sqrt(2h/g) which is identical for both spheres. Therefore the spheres will hit the ground at the same time even though one of the spheres has an initial horizontal velocity and travels a greater distance.

A ball of massΒ *m*Β is in a cup of negligible mass attached to a block of massΒ *M*Β that is on a table.Β A string passing over a light pulley connects the blocks to a 2.5 kg object, as shown above. The cup is a vertical distanceΒ *h*Β off of the floor.Β All friction is negligible.Β In Trial 1, the system is released from rest, the block accelerates to the right, and after moving a distanceΒ *x*Β the block collides with a bumper near the end of the table.Β The ball continues to move and lands on the floor at a position a distanceΒ *d*Β horizontally from where it leaves the cup. In Trial 2, the massΒ *m*Β of the ball in the cup is doubled.Β The system is again released from rest.Β The block collides with the same bumper, the ball continues to move, and lands on the floor.Β In trial 2, does the heavier ball land a horizontal distance from the table that is greater than, less than, or equal toΒ *d*?Β Justify your answer in a clear, coherent, paragraph-length explanation.

Principles

- Falling mass provides the net force to the system (F = ma)
- Mass
*M*and ball travel the same distance on the table (*x*) each trial - Ball goes through projectile motion after it leaves the cup
- Horizontal distance depends on time in air and horizontal velocity
- Height and initial vertical velocity are the same in each trials

Same net force, but more mass in trial 2 --> less acceleration for trial 2

Less acceleration, but same *x* --> less horizontal velocity for trial 2

Same vertical velocity, vertical acceleration and height for both trials --> same time in the air

Less horizontal velocity and same time --> less distance traveled in the air for trial 2

Conclusion - Trial 2's distance will be less than Trial 1's

π₯Watch: AP Physics 1 - Paragraph-Length Responses

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