Question

1. (35 pts) A box (m-0.75 kg) is moving on a horizontal surface with a coefficient of friction of 0.110. A spring with a spring constant of 7.25 N/m is 3.50 m from the box The box is stopped by the spring, compressing it 0.18 m A) What is the initial spood of the box? B) How fast is the box moving when it reaches the spring? Pictorial Representation What is the System? Potential Energies? Nonconservative forces? External Forces? Is Mechanical Energy conserved? Mathematical Representation

Answer 1

system : box and spring

Potential energy = spring potential energy during compression

Non conservative force = Friction

External forces = Friction , gravitational force and normal by ground ( both are perpendicular to motion)

Mechanical energy is not conserved as friction is a non conservative force.

a) Work done by all forces = change in kinetic energy

-friction*d - 0.5kx^2 = 0 - 0.5mv^2 where v is initial velocity

- umgd - 0.5kx^2 = 0 - 0.5mv^2

- 0.11*0.75*9.8*(3.50+0.18) -0.5*7.25*0.18^2 = -0.5*0.75*v^2

v = 2.872 m/s answer

b] again, Work done by all forces = change in kinetic energy

-friction*d = 0.5mv1^2 - 0.5mv^2 where v1 is the velocity at which it strikes

-0.11*0.75*9.8*3.50 = 0.5*0.75*v1^2 -0.5*0.75*2.872^2

- 0.11*0.75*9.8*(3.50+0.18) -0.5*7.25*0.18^2 = -0.5*0.75*v^2

v1 = 0.838 m/s answer