A box with an initial speed of $2 \frac{m}{s}$ $2 m/s$ is moving up a ramp. The ramp has a kinetic friction coefficient of $\frac{1}{2}$ $1/2$ and an incline of $\frac{2 π}{3}$ $(2 pi )/3$ . How far along the ramp will the box go?

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Answer 1 · 2017-07-04T21:53:51

0.331m (3sf)

Resolving perpendicular to the slope:
R=mgcos $(\frac{2 π}{3})$ $((2pi)/3)$
R= $\frac{- m g}{2}$ $(-mg)/2$

F= $μ$ $mu$ R

F= $\frac{- m g}{4}$ $(-mg)/4$

Resolving parallel to the slope:
0 - (F + mgsin $(\frac{2 π}{3})$ $((2pi)/3)$ ) = ma (mass cancels)

Using suvat:
s = $\frac{v^{2} - u^{2}}{2 a}$ $(v^2-u^2)/(2a)$
s = 0.331m

A box with an initial speed of 2ms2 m/s is moving up a ramp. The ramp has a kinetic friction coefficient of 121/2 and an incline of 2π3(2 pi )/3 . How far along the ramp will the box go?