How to find acceleration of object without mass?

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SUMMARY

The acceleration of a ship launched down a ramp at an angle of 8 degrees with a coefficient of kinetic friction of μk=0.06 is calculated using the formula a = gsin(theta) - μkgcos(theta), resulting in an acceleration of 0.8 m/s². The derivation of this equation involves drawing a Free Body Diagram (FBD) and assigning a variable for mass, which ultimately cancels out in the calculations. This approach confirms that mass does not affect the acceleration in this scenario.

PREREQUISITES
  • Understanding of Free Body Diagrams (FBD)
  • Basic knowledge of trigonometric functions (sine and cosine)
  • Familiarity with Newton's second law of motion
  • Concept of kinetic friction and its coefficient
NEXT STEPS
  • Study the derivation of Newton's second law of motion
  • Learn about the role of friction in motion analysis
  • Explore advanced applications of Free Body Diagrams in physics problems
  • Investigate the effects of different angles on acceleration in inclined planes
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for clear examples of acceleration calculations without mass dependence.

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1. A ship is launched into the water down a ramp making an angle of 8 degrees with the horizontal. The coefficient of kinetic friction between the bottom of the ship and the ramp is μk=0.06. What is the acceleration of the ship down the ramp?2. I know that the equation to solve this is
a = gsin(theta) - μkgcos(theta)
Which gives you 0.8 m/s^23. So, I have the equation to solve it and the correct answer but I'm just not sure how to derive that equation in the first place?
 
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Hi grbd920, Welcome to Physics Forums!

Please retain the formatting template headers when you create your homework help requests.

Draw the FBD for the problem and assign a variable, say M, to the mass. Write the equations. You should find that the M cancels out along the way to the solution.
 
gneill said:
Hi grbd920, Welcome to Physics Forums!

Please retain the formatting template headers when you create your homework help requests.

Draw the FBD for the problem and assign a variable, say M, to the mass. Write the equations. You should find that the M cancels out along the way to the solution.
Got it! Thank you! :)
 

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