Question

Suppose you have a (0.750)-kg object on a horizontal surface connected to a spring that has a force constant of (150 N/m). There is simple friction between the object and surface with a static coefficient of friction (mu_s = 0.100). (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and the kinetic coefficient of friction is (mu_k = 0.0850), what total distance does it travel before stopping? Assume it starts at the maximum amplitude.

a) (0.340 m)
b) (0.485 m)
c) (0.620 m)
d) (0.750 m)

Answer 1

The physics question entails calculating the maximum stretch of a spring before moving a mass due to static friction and then finding the total distance travelled by the mass in oscillation with kinetic friction until it stops.

Step-by-step explanation:

This question involves the use of Hooke's Law and the principles of static friction and kinetic energy in the context of a mass-spring system. To address part (a), we need to find the maximum amount of spring stretch that does not exceed the maximum static friction force.

The static friction force can be calculated by multiplying the static coefficient of friction (μs) by the normal force (mass times gravity). Using Hooke's Law (F = kx), we set the spring force equal to the maximum static friction force and solve for x, the stretch distance.

For part (b), when the mass is put into oscillation, it will experience a kinetic friction force opposite to the direction of motion. Since the spring is stretched to twice the x from part (a), we calculate the total work done by the kinetic friction force as the mass moves from maximum amplitude to rest.

Energy conservation will be used here; the initial potential energy stored in the spring (which we calculate using 1/2kx^2) gets converted to work done against friction. By integrating the kinetic friction force over the distance until the mass stops, we get the total distance travelled.