A 300 g block is dropped onto a vertical spring with force constant k = 2.3 N/cm

Question

A 300 g block is dropped onto a vertical spring with force constant k = 2.3 N/cm (Fig. 11-36). The block sticks to the spring, and the spring compresses 13 cm before coming momentarily to rest. (Ignore friction.) (a) While the spring is being compressed, how much work is done on the block by the force of gravity? J b) While the spring is being compressed, how much work is done by the spring? J (c) What is the speed of the block just before it hits the spring? m/s (d) If the speed at impact is doubled, what is the maximum compression of the spring? m

Explanation / Answer

a) w= mg*h= 0.3*9.8*0.13= 0.3822 J

b) w=0.5*k*x^2= 0.5*2.3*10^2*0.13^2= 1.9435 J

c) 1.9435-0.3822= 0.5*0.3*v^2

v=3.23 m/s

d) 0.5*0.3*(2*3.23)^2= 0.5*2.3*10^2*x^2-0.3*9.8*x

6.26=115x^2-2.94x

115x^2-2.94x-6.26=0

x= 0.25 m = 25 cm and -22 cm , max will be 25 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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