A 1.86-kg block is initially held in place against a spring with spring constant

Question

A 1.86-kg block is initially held in place against a spring with spring constant k =2500 N/m (see figure). When released, the block is projected with a speed nu_1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a speed nu_2 = 1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.28. The block moves on to D, where it stops. a) Find the initial compression of the spring? b) Find the height of the ramp, h. c) Use the work-kinetic energy theorem to find S (the distance between points B and D).

Explanation / Answer

a) Using law of conservation of energy

energy stored in spring = energy gained by the block

0.5*k*x^2 = 0.5*m*v1^2

0.5*2500*x^2 = 0.5*1.86*1.2^2

x = 0.0327 m

b) Using law of conservation of energy

0.5*m*v1^2 + m*g*h = 0.5*m*v2^2

m cancels

(0.5*1.2^2)+(9.8*h) = 0.5*1.9^2

h = 0.11 m

C) Work done by the net force = change in kinetic energy

-mu_k*m*g*S = 0.5*m*(V^2-Vo^2)

m cancels

-0.28*9.8*S = 0.5*(0^2-1.9^2)

S = 0.657 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.