Question

A. Situation A: A 20-kg block is pressed against a relaxed spring on a frictionless surface. The spring is compressed by ∆x = 10 cm from its equilibrium position x = x 0 e . The block is released and the spring uncompresses. The speed of the block at x = x 0 e is va,f = 5.0 m/s.

B. Situation B: The same 20-kg block is pressed against two relaxed springs that are attached in series on a frictionless surface. (These two springs are both identical to the spring in Situation A). The entire spring assembly is compressed by ∆x = 10 cm from its equilibrium position x = x 0 e . The block is released and the spring assembly uncompresses. The speed of the block at x = x 0 e is vb,f Question:
What is the value of vb,f ?
(A) 3.5 m/s
(B) 2.5 m/s/s
(C) 5.0 m/s
(D) 6.4 m/s
(E) 7.0 m/s.

Answer 1

E) 7.0 m/s

Step-by-step explanation:

In situation A, by the mean of an energy balance:

`1/2*m*V_a^2-1/2*K*\Delta X^2=0`

Solving for K:

K = 50000 N/m

For situation B:

`1/2*m*V_b^2-1/2*K_t*\Delta X^2=0`

Where
`K_t=K+K=100000N/m`

Replacing this value and solving for Vb:

Vb = 7.07m/s

The answer is option E