Question

A small object is placed at the top of an incline that is essentially frictionless. The object slides down the incline onto a rough horizontal surface, where it stops in 5.0 s after traveling 60 m. a) What is the speed of the object at the bottom of the incline and its acceleration along the horizontal surface? b) What is the height of the incline?

Answer 1

Answer

given,

time taken to stop by the object = 5 s

distance travel before stopping = 60 m

final velocity = 0

using equation of motion

v = u + at

0 = u - 5 a

$a_x = \dfrac{u}{5}$

$s = u t + \dfrac{1}{2}at^2$

$s = 5u + \dfrac{1}{2}\times \dfrac{4}{5}\times u^2$

$60 = 2.5 u$

u = 24 m/s

$a_x = \dfrac{24}{5}$

a_x = 4.8 m/s²

b) using energy conservation

$\dfrac{1}{2}mv_i^2 + \dfrac{1}{2}mv_f^2 = mg(\Delta h)$

$\dfrac{1}{2}v_i^2= g(\Delta h)$

$(\Delta h) = \dfrac{0.5 \times 24^2}{9.8}$

Δh = 29.38 m