Dynamics: Finding force exerted on a box traveling down a slope

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Discussion Overview

The discussion revolves around a physics homework problem involving a pellet sliding down a slope, focusing on determining the force exerted on the pellet by the surface at two specific points. The problem includes considerations of potential energy, kinetic energy, and friction, with an emphasis on the application of conservation of energy principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant calculates the potential energy at point A and attempts to apply conservation of energy to find the velocity at point B, noting the absence of a coefficient of friction as a complication.
  • Another participant requests a sketch to better visualize the problem, indicating a need for clarity in the setup.
  • A different participant emphasizes that the problem requires solving for the friction force at the specified points, suggesting a focus on forces rather than energy alone.
  • One participant mentions a recent announcement from their teacher stating that the problem should be considered without friction, providing a specific answer of 2.55 N but expressing uncertainty about the derivation of this result.

Areas of Agreement / Disagreement

Participants express differing interpretations of the problem, particularly regarding the presence of friction. While one participant suggests solving with friction, another indicates that the problem should be approached as frictionless. There is no consensus on the correct approach or solution.

Contextual Notes

The problem lacks a specified coefficient of friction, which complicates the analysis for some participants. Additionally, the angle between the slope and the horizontal is not explicitly given, which may affect calculations.

jaredogden
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Homework Statement



This is problem 13.70 from Beer and Johnston Vector Mechanics 9th ed.

A 300-g pellet is released from rest at A and slides with friction
along the surface shown. Determine the force exerted on the pellet
by the surface (a) just before the pellet reaches B, (b) immediately
after it has passed through B.

The drawing shows a pellet A on a declining slope, distance 1.2 m to B which is almost at the bottom of the slope. C is a flat surface. The radius of curvature between B and C is 0.8 m and the angle between them is 30°

Homework Equations



PE = mgz
KE = 1/2mv2
Fr = muk*N
Energy from Fr = FrΔx

The Attempt at a Solution



Since the pellet is at rest KEA = 0J, however PEA = (.3kg)(9.81m/s2)(1.2sin(30°))
(The angle between the horizontal and the 1.2m hypotenuse isn't given, but I just found it using opposite interior angles.)

so PEA = 1.7658 J

At B we will have KE and PE. Assuming C is at z = 0m we can use the radius of curvature and angle given to find zb

zB = 0.8 m - 0.8 m * cos(30°)
zB = 0.10718 m

so PEB = (.3kg)(9.81m/s2)(0.10718 m)
PEB = 0.31543 J

KEB = 1/2(.3 kg)vB2

Plugging all of this into the law of conservation of energy where EA = EB

1.7658 J = 0.31543 J + (1/2)(.3 kg)vB2
vB = 3.109 m/s

I got hung up here because I think that the work due to the frictional force should be subtracted from KEB + PEB in order to get the correct velocity the pellet would be traveling at. However, there is no coefficient of friction given in the problem.

I feel like I'm just missing something small here and my brain is just dead..
 
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Would you sketch this?
 
It is problem 13.70
 

Attachments

From my reading of the problem, you're supposed to solve for the friction force on the block at the given points.
 
Our teacher just posted an announcement that the problem should be a pellet sliding without friction.

The answer is 2.55N, I'm just unsure how to get here..
 

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