A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s.It is brought to rest by compressing a very long spring of spring constant 800 N/m.The maximum spring compression is:
A)0.6 cm
B)3 cm
C)5 cm
D)7 cm
E)8 cm

Question

Quizplus · Accepted Answer

The initial kinetic energy of the block is given by:
Kinitial = (1/2)mv^2 = (1/2)(0.5 kg)(2 m/s)^2 = 1 J

The final potential energy stored in the compressed spring is given by:
Ufinal = (1/2)kx^2
where x is the maximum compression of the spring.

Since energy is conserved, we have:
Kinitial = Ufinal

Substituting the values, we get:
1 J = (1/2)(800 N/m)x^2
x^2 = 0.0025 m^2 = (0.05 m)^2

Taking the square root, we get:
x = 0.05 m = 5 cm

Therefore, the maximum spring compression is 5 cm.

A 05-Kg Block Slides Along a Horizontal Frictionless Surface at 2