Conservation of Energy on a frictionless incline

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SUMMARY

The discussion centers on calculating the minimum initial speed required for a 259 g textbook to slide up a 22.1° frictionless incline measuring 2.55 m. The correct approach involves using the conservation of energy principle, equating kinetic energy (KE) and potential energy (PE). The user initially miscalculated the height using the incorrect angle of 21.5°, leading to an incorrect initial speed of 4.27 m/s. Upon correcting the angle to 22.1°, the accurate initial speed is confirmed to be 4.34 m/s.

PREREQUISITES
  • Understanding of kinetic energy (KE) and potential energy (PE) equations
  • Basic trigonometry for calculating height on an incline
  • Familiarity with the concept of conservation of energy
  • Knowledge of gravitational acceleration (9.8 m/s²)
NEXT STEPS
  • Review the principles of conservation of energy in physics
  • Study trigonometric functions and their applications in physics problems
  • Learn about the effects of friction on energy conservation
  • Explore advanced problems involving inclined planes and energy transformations
USEFUL FOR

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

Ly444999
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Homework Statement


A 259 g textbook slides up a 22.1° incline that is 2.55 m long. Using conservation of energy and assuming the incline is frictionless, what minimum initial speed is needed to accomplish this?
mass = 0.259 kg
Θ = 22.1°
length of incline = 2.55 m

Homework Equations


KE = (1/2)*mv2
PE = mgh

The Attempt at a Solution


I solved for height of the incline/ramp using trigonometry where the height is opposite to the angle and the length of the ramp is the hypotenuse:
h = 2.55*sin(21.5°) = 0.934

Since the incline is frictionless the kinetic energy at the beginning is equal to the potential energy of when the textbook reaches the top of the ramp:
KE = PE
(1/2)*mv2 = mgh
Isolating for the velocity, the masses cancel out
v = √2gh
v = √(2*9.8*0.934)
= 4.27 m/s

So I got 4.27 m/s as initial velocity but it doesn't match with any of the answers which are either 4.34 m/s, 7.07 m/s, 3.07 m/s or 6.80 m/s.

So I was wondering what I did wrong. Was the velocity I was solving for not initial velocity or was the approach completely wrong? or Did I just make some miscalculations that made it not equal to the first answer?
 
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Ly444999 said:
a 22.1° incline

Ly444999 said:
sin(21.5°)

Notice anything?
 
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haruspex said:
Notice anything?
****, ok I'm very unintelligent, for some reason in my calculations I'm using 21.5 as my degrees I don't know why, thank you for pointing out my obvious mistake though lol.
Edit: I got right answer thank you lol.
 

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