Unbalances and balanced forces

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The discussion focuses on calculating the time it takes for a 13 kg box to slide down a 4.5 m ramp inclined at 41 degrees, with a coefficient of friction of 0.19. The gravitational force acting on the box is calculated to be 127 N, with a component of 83 N acting down the ramp. The acceleration of the box is determined to be 6.4 m/s², leading to a calculated time of 1.19 seconds to reach the bottom of the ramp. The role of friction in this scenario is highlighted, emphasizing the need to consider both gravitational and frictional forces in the analysis.

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A 13 kg box is placed at the top of a 4.5 m long, ramp inclined at an angle of 41 degrees (with the horizon). However, the ramp is covered with sand so the coefficient of friction is 0.19. How much time does it take the box to reach the bottom of the ramp?



Fgx=Fg sin=mg sin.




13kg (9.8 N/kg)=127N

127N Sin 41= 83N

Acceleration=83N/13kg=6.4m/s

4.5m=1/2 (6.4m/s)t^2

4.5m=3.2m/s t^2
t=1.19s
Im just confused as where the coefficient of friction comes into play, and how to solve it.
 
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As the box travels down the ramp, there is a frictional force on it and well as the gravitational force.
Draw the free-body diagram and work out the net force on the box down the ramp.
 

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