A 250-g metal cube connected to a light spring of constant 35 N/m oscillates on a horizontal,frictionless surface.The maximum velocity is 0.98 m/s.What is the amplitude of its motion?
A)7.0 cm
B)4.0 cm
C)8.3 cm
D)9.1 cm
E)5.3 cm

Question

Quizplus · Accepted Answer

The maximum velocity of the object occurs when all of the potential energy is converted to kinetic energy and vice versa. Using conservation of energy:

1/2 k A^2 = 1/2 mv^2

Where k is the spring constant, A is the amplitude, m is the mass of the object, and v is the maximum velocity.
Plugging in the given values, we get:

1/2 (35 N/m) A^2 = 1/2 (0.25 kg) (0.98 m/s)^2

Simplifying and solving for A, we get:

A = 0.083 m = 8.3 cm

Therefore, choice C is the best answer.

A 250-G Metal Cube Connected to a Light Spring of Constant