A 20-g object is placed against the free end of a spring (k equal to 20 N/m) tha

Question

A 20-g object is placed against the free end of a spring (k equal to 20 N/m) that is compressed 11.2 cm (figure below). Once released, the object slides 1.25 m across the tabletop and eventually lands 1.60 m from the edge of the table on the floor, as shown. Is there friction between the object and the tabletop? If there is, what is the coefficient of kinetic friction? The sliding distance on the tabletop includes the 11.2-cm compression of the spring and the tabletop is 1.00 m above the floor level.

Explanation / Answer

given,

mass of object = 20 gm or 0.02 kg

spring constant = 20 N/m

spring is compressed by 11.2 cm or 0.112 m

object slides by 1.25 m and lands at 1.6 m from edge

height of the table = 1 m

time taken by object to fall 1 m be t

by second equation of motion

s = ut + 0.5 at^2

since initial vertical velocity will be 0

1 = 0 + 0.5 * 9.8 * t^2

t = 0.4517 sec

horizontal speed = horizontal distance / time

horizontal speed = 1.6 / 0.4517

horizontal speed = 3.542 m/s

by conservation of energy

initial energy = final energy

initial energy = 0.5 * kx^2

initial energy = 0.5 * 20 * 0.112^2

initial energy = 0.1254 J

final energy = 0.5 * mv^2

final energy = 0.5 * 0.02 * 3.542^2

final energy = 0.1254

since, initial energy = final energy there is no loss of energy due to friction so,

there is no friction between the object and table top

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