Block going up a frictionless incline

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SUMMARY

A 2.6 kg block slides on a frictionless surface at 2.9 m/s before transitioning to a frictionless ramp inclined at 12 degrees. Using the conservation of mechanical energy, the initial kinetic energy of the block can be equated to the potential energy at the maximum height reached on the ramp. The relationship between height and distance up the ramp can be established using trigonometric functions, allowing for the calculation of how far the block slides up the incline before coming to rest.

PREREQUISITES
  • Understanding of conservation of mechanical energy
  • Basic knowledge of trigonometry, particularly relating angles to distances
  • Familiarity with kinematic equations
  • Concept of frictionless surfaces and their implications in physics
NEXT STEPS
  • Calculate the maximum height reached using the equation for conservation of mechanical energy
  • Convert the height to distance up the ramp using trigonometric functions
  • Explore the implications of varying the angle of incline on the distance traveled
  • Investigate the effects of friction on similar problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to enhance their teaching methods in these areas.

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Homework Statement



A 2.6kg block slides along a frictionless horizontal with a speed of 2.9m/s. After sliding a distance of 6m, the block makes a smooth transition to a frictionless ramp inclined at an angle of 12 degrees to the horizontal. How far up the ramp does the block slide before coming momentarily to rest?


Homework Equations



Conservation of mechanical energy...1/2mv0^2 + mgh0 = 1/2mvf+mghf.



The Attempt at a Solution



I know that V0 = 26, Vf = 0, but I don't know what h is. Is there another approach to this problem?

Thank you so much!
 
Physics news on Phys.org
Realize that you can express the final position in terms of height or distance up the ramp: those two distances are connected by a little trig.

In any case, you can solve for the final height, then convert to the needed distance up the ramp.
 

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