The ramp
A 5kg package is pushed 2m up a ramp that is inclined at 12 degrees above the horizontal, by a 100N force that is parallel to the ramp. The coefficient of kinetic friction between the package and the ramp is 0.3. If the package started from rest, what was its speed after sliding 2m up the ramp?
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1 solution
W f o r c e = F ( s ) = 1 0 0 N ( 2 m ) = 2 0 0 J
W f r i c t i o n f o r c e = ( − 0 . 3 ) ( 5 ) ( 9 . 8 c o s 1 2 ) ( 2 ) = − 2 8 . 7 5 7 5 J
W w e i g h t = − ( m g s i n θ ) ( s ) = − ( 5 ) ( 9 . 8 s i n 1 2 ) ( 2 ) = − 2 0 . 7 3 5 3 J
W n o r m a l f o r c e = 0
W t o t a l = W f o r c e + W f r i c t i o n f o r c e + W w e i g h t + W n o r m a l f o r c e
= 1 5 0 . 8 6 7 2 J
W t = 2 1 ( m ) ( V f i n a l 2 − V i n i t i a l 2 )
1 5 0 . 8 6 7 2 J = 2 1 ( 5 ) ( V f i n a l 2 − 0 )
V f i n a l = 7 . 7 6 8 3