Question

A crate is given an initial speed of 2.2 m/s up the 22.5 ∘plane shown in (Figure 1). Assume μk = 0.12.

How far up the plane will it go?

Express your answer to two significant figures and include the appropriate units.

How much time elapses before it returns to its starting point?

Express your answer to two significant figures and include the appropriate units.

Answer 1

initial speed u = 2.2 m / s

angle of inclinationm = 22.5^o

coefficient of kinetic friction μ_k = 0.12

(a)

the displacement up the incline will be

s = u² / 2g (sin + μ_k cos)

(b)

it reaches the starting point after the time interval t

t = t_a + t_d

t_a = time of ascent

t_d = time of decent

t_a = u / g (sin + μ_k cos)

= 0.454

remember that time of ascent is not equal to time of descent

t_d = sqrt{2 s / g (sin - μ_k cos) }

t_d = 0.642

t = t_a + t_d

_{= 0.454+0.642 = 1.096 s}