Block moving down circle, a straight path, then into a spring

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SUMMARY

The discussion revolves around a physics problem involving a block sliding down a frictionless circular track and compressing a spring. The key calculations include determining the velocity at point B using the equation ƩF=mv²/r, calculating the thermal energy produced due to kinetic friction between points B and C, and finding the velocity at point C. Additionally, the stiffness constant k of the spring is to be determined after the block compresses it by 0.35 meters. The coefficient of kinetic friction is specified as 0.27, and the radius of the circular track is 2.0 meters.

PREREQUISITES
  • Understanding of Newton's second law and centripetal force (ƩF=mv²/r)
  • Knowledge of energy conservation principles (potential and kinetic energy)
  • Familiarity with the concept of kinetic friction and its effects on motion
  • Basic understanding of spring mechanics and Hooke's Law
NEXT STEPS
  • Calculate the velocity at point B using energy conservation principles.
  • Determine the thermal energy produced during the block's motion from B to C.
  • Calculate the velocity at point C after accounting for friction.
  • Find the spring constant k using the compression distance and energy principles.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy transformations, as well as educators looking for practical examples of energy conservation and friction in motion.

bfusco
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Homework Statement


Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 and is frictionless. B to C is a horizontal span 3.5 long with a coefficient of kinetic friction = 0.27. The section CD under the spring is frictionless. A block of mass 1.0 is released from rest at A. After sliding on the track, it compresses the spring by 0.35 .
A)calculate the velocity at point B.
B)Determine the thermal energy produced as the block slides from B to C.
C)calculate the velocity at point C.
D)determine the stiffness constant k for the spring.

Homework Equations





The Attempt at a Solution


A) i am having a hard time starting this question. for part A, i draw the free body diagram at the the top of the diagram (the side of the circle), i have the Normal force facing the center of the circle and the weight facing down. with that said i don't understand how to begin ƩF=mv^2/r equation in order to calculate the velocity.

 
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bfusco said:

Homework Statement


Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 and is frictionless. B to C is a horizontal span 3.5 long with a coefficient of kinetic friction = 0.27. The section CD under the spring is frictionless. A block of mass 1.0 is released from rest at A. After sliding on the track, it compresses the spring by 0.35 .
A)calculate the velocity at point B.
B)Determine the thermal energy produced as the block slides from B to C.
C)calculate the velocity at point C.
D)determine the stiffness constant k for the spring.

Homework Equations





The Attempt at a Solution


A) i am having a hard time starting this question. for part A, i draw the free body diagram at the the top of the diagram (the side of the circle), i have the Normal force facing the center of the circle and the weight facing down. with that said i don't understand how to begin ƩF=mv^2/r equation in order to calculate the velocity.

OK try these clarifying questions.

What energy transformation(s) occur in the A - B section?

What energy transformation(s) take place in the B - C section?

What energy transfer takes place after C?
 
PeterO said:
OK try these clarifying questions.

What energy transformation(s) occur in the A - B section?

What energy transformation(s) take place in the B - C section?

What energy transfer takes place after C?

from A - B the potential energy would go from its greatest value to 0, all that energy would become kinetic energy.

from B - C, the kinetic energy would decrease due to work done by friction.

after C, the object would hit the spring creating elastic potential energy.

Sorry about the lack of clarity, was in a rush when i posted and I am new at communicating over forums.
 
bfusco said:
from A - B the potential energy would go from its greatest value to 0, all that energy would become kinetic energy.

from B - C, the kinetic energy would decrease due to work done by friction.

after C, the object would hit the spring creating elastic potential energy.

Sorry about the lack of clarity, was in a rush when i posted and I am new at communicating over forums.

NO NO NO

The question was perfectly clear to me - and if you understand what you have just written, then you should be able to solve the problem
 

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