AP Physics 1 Unit 2 Progress Check provides detailed solutions to free-response questions focusing on circular motion, forces, and friction. It includes derivations of tension in strings and the relationship between spring constants and maximum stretch. This resource is essential for AP Physics students preparing for exams, offering clear explanations and step-by-step problem-solving techniques. The content covers key concepts such as Newton's laws, tension in circular motion, and the principles of friction, making it a valuable study aid for mastering physics concepts.

Key Points

  • Includes solutions to AP Physics 1 Unit 2 free-response questions.
  • Derives expressions for tension in strings during circular motion.
  • Explains the relationship between spring constants and maximum stretch.
  • Covers key concepts in forces, friction, and circular motion.
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AP® Physics 1
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1.
Show all your work for each part of the question. The parts within the question may not have equal weight.
A sphere of mass is attached to a string of length . The sphere swings in a horizontal circle with a constant⯑
speed, as shown in Figure . The string makes an angle with the vertical.
(a)
i. On the following dot, which represents the sphere, , and label the forces that act on the sphere when thedraw
sphere is at the position shown in Figure . Each force must be represented by a distinct arrow starting on, and
pointing away from, the dot. Draw the relative lengths of the vectors to reflect the relative magnitudes of the
forces exerted on the sphere for any relative values known.
AP PHYSICS 1 Scoring Guide
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ii. Starting with Newton’s second law, an expression for the speed of the sphere. Express your answerderive
in terms of , , , and physical constants, as appropriate. Begin your derivation by writing a fundamental⯑
physics principle or an equation from the reference booklet.
(b) A student claims that if the sphere is swung ball fast enough, the string will be perfectly horizontal. Indicate
whether this claim is correct or incorrect and your answer.justify
Part A
Select a point value to view scoring criteria, solutions, and/or examples and to score the response.
0 1 2 3 4 5 6 7
The response accurately includes the following criteriaall
1 point is earned for drawing a downward arrow labeled as the gravitational force.
1 point is earned for a drawing an arrow that points along the direction of the string labeled as the tension
force.
Example Response
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Scoring Note: Examples of appropriate labels for the force due to gravity include , , , “grav
force,” “ Earth on sphere,” “ on sphere by Earth,” , , . The
labels or are not appropriate labels for the force due to gravity.
Scoring Note: Examples of appropriate labels for the tension force include , , , Force from string.
1 point is earned for a multi-step derivation starting with Newton’s second law.
1 point is earned for attempting to find the components of the force of tension.
Scoring Note: The trigonometry does not have to be correct to earn this point.
1 point is earned for the substitution of for the acceleration in the horizontal direction.
1 point is earned for of the following:ONE
◦ Solving two Newton’s Laws equations for tension and setting them equal to each other
◦ Solving one Newton’s Law equation for tension and substituting that expression into a second
Newton’s law equation
1 point is earned for a correct expression for the speed of the ball in terms of given variables.
Example Response:
Scoring Guide
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FAQs

What is the significance of tension in circular motion?
Tension plays a crucial role in maintaining the circular motion of an object. When an object moves in a circle, the tension in the string provides the necessary centripetal force to keep the object on its circular path. As the speed of the object increases, the tension must also increase to counterbalance the gravitational force and provide the required net force for circular motion. Understanding this relationship helps in analyzing various physical scenarios involving circular dynamics.

How is the coefficient of kinetic friction derived in this context?
The coefficient of kinetic friction is derived by analyzing the forces acting on an object sliding down an inclined plane. By applying Newton's second law, the net force can be expressed in terms of the gravitational force and the frictional force. The relationship between the normal force and the gravitational force leads to the formulation of the coefficient of kinetic friction, which is crucial for understanding motion on surfaces with friction.

What are the main topics covered in the AP Physics 1 Unit 2 Progress Check?
The main topics include circular motion, tension in strings, and the effects of friction on motion. Students will explore how forces interact in circular motion, derive equations for tension based on speed and mass, and examine the principles of kinetic and static friction. This comprehensive coverage ensures that students are well-prepared for the AP Physics exam.

What types of problems are included in the Unit 2 Progress Check?
The Unit 2 Progress Check includes a variety of free-response problems that challenge students to apply their understanding of physics concepts. Problems may involve calculating tension in a string during circular motion, analyzing forces on an inclined plane, and deriving expressions for frictional forces. These problems are designed to test critical thinking and problem-solving skills essential for success in AP Physics.

How does the tension in a string change with varying speeds in circular motion?
As the speed of an object in circular motion increases, the tension in the string must also increase to maintain the circular path. This is due to the need for a greater centripetal force, which is provided by the tension. If the speed doubles, the required tension increases by a factor of four, illustrating the quadratic relationship between speed and tension in circular motion.