A 20-g object is placed against the free end of a spring (k equal to 24 N/m) tha

Question

A 20-g object is placed against the free end of a spring (k equal to 24 N/m) that is compressed 10.2 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 10.2-cm compression of the spring and the tabletop is 1.00 m above the floor level.

Explanation / Answer

Let, y = 1 m

x = 1.6 m

Let t is the time taken to fall down for the object.

Apply, -y = voy*t - (1/2)*g*t^2

-y = -(1/2)*g*t^2 (since voy = 0)

t^2 = 2*y/g

t = sqrt(2*y/g)

= sqrt(2*1/9.8)

= 0.4517 s

speed of block when it leaves the table, v = x/t

= 1.6/0.4517

= 3.54 m/s

Let u is the speed of the block when it leaves the spring,(If friction is not present)

Apply Energy conservation

0.5*m*u^2 = 0.5*k*x^2

u = x*sqrt(k/m)

= 0.102*sqrt(24/0.02)

= 3.54 m/s

speed of the block when it leaves the spring = speed of the block when leaves the tabel.

so, there is no friction.

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