Energy conservation of a sliding box

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SUMMARY

The discussion focuses on calculating the distance a 3.4 kg rock slides on a horizontal surface after descending a 25 cm incline at a 33-degree angle, with a friction coefficient of 0.19. The user employs the energy conservation equation, specifically .5MVi² + MGy1 = .5MVf² + MGy2 + Ffrd, to determine the initial velocity at the bottom of the incline. After calculating the incline length as 0.459 meters and the velocity at the bottom as 1.861 m/s, the user attempts to find the sliding distance but initially arrives at an incorrect value of 31.01425 meters.

PREREQUISITES
  • Understanding of energy conservation principles in physics
  • Familiarity with kinematic equations
  • Knowledge of friction coefficients and their impact on motion
  • Basic trigonometry for calculating incline lengths
NEXT STEPS
  • Review the derivation of the energy conservation equation in mechanics
  • Learn how to calculate the effects of friction on motion using Ffr = μN
  • Study kinematic equations to better understand motion on inclined planes
  • Explore the relationship between angle of incline and gravitational components
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to explain concepts of motion and friction in real-world scenarios.

utsharpie
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3.4kg rock starts at 25 cm on a plane with a 33degree angle. upon reaching the bottom the box slides along the horizontal. friction coeff is
.19. how far does the box slide on the horizontal before coming to a rest?

ok i need to use .5MVi2 + MGy1 = .5MVf2 + MGy2 + Ffrd

first i need to find the velocity of the box as it hits the end of the incline. i also need the length of the incline.

i have Y1=.025 meters
Vf=0
Vi=0
M=3.4kg
g=9.8
theta=33
fr=.19

i keep getting 4.3 meters but its wrong
 
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ok i found the distance from top of incline to bottom of incline to be .459meters using laws of triangles. so if friction is acting the velocity is gsin33-.19gcos33 and that equals 3.7758

v2=2ad
v2=3.466
v=1.8618

ok so we got Vi at the bottom to be 1.861 and the y1 and y2 at the bottom are both zero and the final V is 0. so is it mv2/2=.19d? and that comes out to 31.01425 meters?no way!
 

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