Find how long a marble rolls down a ramp, given distance and angle

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SUMMARY

The discussion focuses on calculating the time it takes for a marble to roll down a ramp measuring 5.0 meters in length at an angle of 6.9°. The correct answer is established as 2.9 seconds. Key equations used include v = at and d = 1/2at², with emphasis on determining the acceleration component along the ramp due to the angle. Participants highlight the importance of the ramp's angle in affecting the marble's descent time.

PREREQUISITES
  • Understanding of basic physics concepts such as acceleration and motion.
  • Familiarity with kinematic equations, specifically d = 1/2at².
  • Knowledge of trigonometry to resolve components of forces based on angles.
  • Ability to apply Newton's laws of motion in practical scenarios.
NEXT STEPS
  • Learn how to resolve forces using trigonometric functions in inclined planes.
  • Study the effects of different angles on acceleration and time in motion problems.
  • Explore the concept of rolling motion and its equations of motion.
  • Investigate the impact of friction on the motion of objects rolling down ramps.
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding motion dynamics on inclined planes.

camelCaseD
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Homework Statement


How many seconds does it take a marble to run down a ramp with a length of 5.0 m and an angle of 6.9°?
Correct answer = 2.9 s.

Homework Equations


v = at
d = 1/2at2

The Attempt at a Solution


√2(5)/9.8≠2.9 s
 
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hi camelCaseD! welcome to pf! :smile:

where did you use the 6.9° ? :confused:

(or the fact that it rolls)
 
I'm not sure if the angle is relevant information for solving the problem or not. But the length of the ramp and the angle its at are the only given data I have. The marble does roll down the ramp.
 
camelCaseD said:
I'm not sure if the angle is relevant information for solving the problem or not.

?? :confused: but if this 5m ramp was at 0.01°, wouldn't it take a lot longer than if it was at 90° ?
 
tiny-tim said:
?? :confused: but if this 5m ramp was at 0.01°, wouldn't it take a lot longer than if it was at 90° ?
Yes it would be slower if the angle were 0.01° than 90°.
 
yes! :smile:

sooo … ? :wink:​
 
So then since the angle of the ramp is at 6.9° the time it would take the marble to roll down the ramp would take longer than if it were straight up and down.
 
yes, but what equation are you going to use?

(and now I'm off to bed :zzz:)
 
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I'm going to use the equation d=1/2at2
 
  • #10
(just got up :zzz:)
camelCaseD said:
I'm going to use the equation d=1/2at2

yeeees …

but first you need to find a (the component of acceleration down the ramp)!​

what equation will you use for that? :smile:
 

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