Question

Choose the correct answer.

A small sphere attached to the extremity of a spring of constant 25 N/m has a maximum kinetic
energy of 0.5 J as it passes by the position of equilibrium. Determine the maximum displacement of
the spring.
A) 10 cm
B) 4 cm
C) 20 cm
D) 2 cm

Answer 1

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>>A block of mass m = 2.0 kg is dropped fr

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A block of mass m=2.0kg is dropped from height h=40cm onto a spring of spring constant k=1960N/m (Fig. 8-39). Find the maximum distance the spring is compressed.

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Updated on : 2022-09-05

Solution

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We denote m as the mass of the block, h=0.40m as the height from which it dropped (measured from the relaxed position of the spring), and x as the compression of the spring(measured downward so that it yields a positive value). Our reference point for the gravitational potential energy is the initial position of the block. The block drops a total distance h+x, and the final gravitational potential energy is –mg(h+x).

The spring potential energy is

2

1

kx

2

in the final situation, and the kinetic energy is zero both at the beginning and end. Since energy is conserved

K

i

+U

i

=K

f

+U

f

0=−mg(h+x)+

2

1

kx

2

which is a second-degree equation in x. Using the quadratic formula, its

solution is

x=

k

mg±

(mg)

2

+2mghk

Now

mg=19.6N,h=0.40m, and k=1960N/m, and we choose the positive root so that x>0.

x=

1960

19.6+

19.6

2

+2(19.6)(0.40)(1960)

=0.10m.