Question

Someone at the other end of the table asks you to pass the salt. Feeling quite dashing, you slide the 50.0-g salt shaker in that direction, giving it an initial speed of 1.15 m/s. (a) If the shaker comes to rest with constant acceleration in 0.840 m, what is the coefficient of kinetic friction between the shaker and the table? (b) How much time is required for the shaker to come to rest if you slide it with an initial speed of 1.32 m/s?

Answer 1

(a) The coefficient of kinetic friction between the shaker and the table is 0.08.

(b) The time taken for the shaker to come to rest is 1.7 seconds.

How to calculate the coefficient of friction?

(a) The coefficient of kinetic friction between the shaker and the table is calculated by applying the principle of work energy theorem.

W = K.E

μmgd = ¹/₂mv²

μgd = ¹/₂v²

μ = v² / 2gd

where;

• v is the speed of the salt shaker
• g is acceleration due to gravity
• d is the distance traveled

μ = v² / 2gd

μ = (1.15)² / (2 x 9.8 x 0.84)

μ = 0.08

(b) The acceleration of the shaker is calculated as follows;

a = μg

a = 0.08 x 9.8 m/s²

a = 0.78 m/s²

The time taken for the shaker to come to rest is calculated as;

v = u - at

when the shaker comes to rest, the final velocity = 0

0 = u - at

at = u

t = u / a

t = (1.32 m/s) / (0.78 m/s²)

t = 1.7 seconds