A 200 g block is dropped onto a vertical spring with force constant k = 2.1 N/cm

Question

A 200 g block is dropped onto a vertical spring with force constant k = 2.1 N/cm (Fig. 11-36). The block sticks to the spring, and the spring compresses 11 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?
0.2156 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) work done on the block by the force of gravity

= mgh

= 0.2*9.8*0.11 = 0.2156 J

b) work done by the spring = 0.5kx^2 = 0.5*210*0.11^2 = 1.2705 J

c) speed of the block = sqrt(2K/m)

v = sqrt(2*(1.2705+0.2156) / 0.2 )

v = 3.854 m/s

d) 0.5mv^2 = 0 .5kx^2

x is propotional to v

so , when v is doubled x will also be doubled

maximum compression = 22 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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