Starting with an initial speed of 5.00 m/s, a 10.00 kg piece of luggage slides 6

Question

Starting with an initial speed of 5.00 m/s, a 10.00 kg piece of luggage slides 6.00 m down a rough 40 degree incline. Then it slides along a horizontal surface for some distance. The coefficient of kinetic friciton between the luggage and the surface is 0.300 for both the incline and the horizontal. Assume the luggage has a smooth transition form the incline to the horizontal.

A) Determine the speed of the luggage as it reaches the bottom of the incline.

B) Using the value of the speed from part A, calculate how far the luggage will slide along the horizontal.

Explanation / Answer

Here ,

let the initial speed = 5 m/s

at the bottom of the incline , let the speed is v m/s

Usinng conservation of energy

0.5* m * u^2 + m * g * h= 0.5 * m * v^2 + u * mg * (h/sin(theta))

0.5 * 5^2 + 9.8 * 6 = 0.5 * v^2 + 0.3 * 9.8 * 6/sin(40)

soving for v

v = 9.37 m/s

the speed of box at the bottom is 9.37 m/s

B)

acceleration , a = -u * g

a = -9.8 * 0.3

a = -2.94 m/s^2

let the distance is d

d = v^2/(2 * a)

d = 9.37^2/(2 * 2.94)

d = 11.93 m

the lauggage will slide along the horizontal is 11.93 m

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