Question

Consider a 3.0 kg mass on a spring on a horizontal surface. The spring has spring constant 45 N/m. The static coefficient of friction between the mass and the surface is µS = 0.30 and the kinetic coefficient of friction is µK = 0.20

(a) When the mass is at x0 = 20 cm it is moving to the right with speed 50 cm/s. Where does it first come to a stop? [Hint: use energy considerations.]

(b) Once the mass stops, does it remain at rest or does it move back to the left? If it moves to the left, what is its initial acceleration? Justify your answer.

05.3 Consider a 3.0 kg mass on a spring on a horizontal surface. The spring has spring constant 45 N/m. The static coefficient of friction between the mass and the surface is us 0.30 and the kinetic coefficient of friction is uK 0.20 Equilibrium position (a) When the mass is at xo 20 cm it is moving to the right with speed 50 cm/s. Where does it first come to a stop? LHint: use energy considerations.] (b) Once the mass stops, does it remain at rest or does it move back to the left? If it moves to the left, what is its initial acceleration? Justify your answer.

I just don't know where to begin, or what equations that I should be using.

Answer 1

Solution:- a) Using conservation of total energy, Kinetic energy elastic potential energy-final elastic potential energy + work done by friction (0.5) (3) (0.50). (0.5) (45) (0.20)-(0.5) (45)そ2 + (0.20) (3) (9.8) (0.2 +%) Solve for 0.016 m1.6 cm

b) f-static frictional force acting at rest 0.30 x 3 x 9.8 -8.82 N Fspring force 45 (0.016) -0.72< Hence the block will remain at rest.