Physics question

Question

Consider a  block that is dragged by a spring on a (relatively) frictionless horizontal surface at constant velocity. Suppose the block reaches a rough patch and the spring stretches by . Compute the coefficient of kinetic friction  between the block and the rough patch if the spring has a force constant 

Answer 1

Hello Eunjin L

On a horizontal surface, normal reaction R = Weight = 5.45 x 9.81 = 53.46N

force of kinetic friction = µ x R

Also the applied force stretches the spring by 4.25cm/100=0.0425m

Since Force causing this stretch = k⋅x

substituting in the formula for force of friction,

k•x = µ•R

∴ µ = 0.0425k/53.46. If a numerical value of spring constant k is known, it can be substituted to determine a numerical value of µ.