What Is the Box's Speed at t = 0.6?

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SUMMARY

The problem involves a 6 kg box sliding down a frictionless incline at a 34-degree angle, starting from a height of 17 m. The acceleration due to gravity is 9.81 m/s². To find the box's speed at t = 0.6 seconds, the conservation of mechanical energy cannot be directly applied since the box has not reached the bottom of the incline. Instead, one must resolve the gravitational force into components to determine the acceleration parallel to the incline and then apply the formula v = v0 + a*t, where v0 is the initial speed (0 m/s).

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of gravitational force components
  • Familiarity with kinematic equations
  • Basic principles of conservation of mechanical energy
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  • Study how to resolve forces into components on inclined planes
  • Learn about kinematic equations for uniformly accelerated motion
  • Explore the concept of acceleration due to gravity on different surfaces
  • Practice problems involving conservation of energy in non-conservative systems
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the_d
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A 6 kg box slides down a long, frictionless
incline of angle 34 degrees. It starts from rest at time
t = 0 at the top of the incline at a height 17 m
above the ground. The acceleration of gravity is 9.81 m/s^2 :Find the box's speed at t = 0.6.

to do this problem i used the conservation of mechanical energy formula and just solved for v #2 squared but apparently that wasnt right
 
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the_d said:
A 6 kg box slides down a long, frictionless
incline of angle 34 degrees. It starts from rest at time
t = 0 at the top of the incline at a height 17 m
above the ground. The acceleration of gravity is 9.81 m/s^2 :Find the box's speed at t = 0.6.

to do this problem i used the conservation of mechanical energy formula and just solved for v #2 squared but apparently that wasnt right
You can't directly use Conservation of Energy with the (17 meter) incline height because the box has NOT slid down to the bottom in (t = 0.6 sec). Instead, try resolving the force of gravity into components parallel and perpendicular to the slide, determine the box's acceleration "aparallel" parallel to the incline, and then use the formula below at (t = 0.6 sec) with (v0 = 0):
vparallel(t) = v0 + aparallel*t


~~
 
thanx xanthym
 

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