5) (Adapted from problem by Kesten & Tauck) A 20.0 g object is placed against th

Question

5) (Adapted from problem by Kesten & Tauck) A 20.0 g object is placed against the free end of a spring (k equal to 25.0 N/m) that is compressed 10.0 cm. 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 10.0 cm compression of the spring. The table is at a height of 1.00 m above the floor level. 1.25 m 10000 1.00 m 1.60 m

Explanation / Answer

The time needed to fall 1 meter off the table is

h = ½gt²

t = (2h/g)

t = (2(1)/9.81)

t = 0.4515 s

traveling the horizontal distance in that time means the object was traveling

v = 1.6 / 0.4515

v = 3.544 m/s

when it left the edge of the table (neglecting air resistance)

The kinetic energy at the edge of the table will equal the spring potential minus the friction work

KE = PS - U

½mv² = ½kx² - Fd

½mv² = ½kx² - (mg)d

= (kx² - mv²) / (2mgd)

|| = (25.0(0.1)² - 0.020(3.544)²) / (2(0.020)9.81(1.25))

|| = 0.00244

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