A block starts from rest at the top of a 31.0° inclined plane and encounters a spring,of constant 3.4 kN/m,rigidly attached to the plane.If the block's mass is 33.0 kg and it compresses the spring by 37.0 cm,find the distance the block travelled before it encountered the spring.
A)1.0 m
B)137 cm
C)74 m
D)82.6 cm

Question

Quizplus · Accepted Answer

The correct answer is A because the block's initial potential energy is converted into kinetic energy and then into spring potential energy. The distance traveled before encountering the spring can be found using the conservation of energy:$$mgh = (1/2)mv^2 + (1/2)kx^2$$where m is the mass of the block, g is the acceleration due to gravity, h is the height of the inclined plane, v is the velocity of the block before encountering the spring, k is the spring constant, and x is the compression of the spring.Solving for h, we get:$$h = (v^2/2g) + (kx^2/2mg)$$Substituting the given values, we get:$$h = (0^2/2g) + (3.4 kN/m * (0.37 m)^2/2 * 33.0 kg * 9.81 m/s^2)$$$$h = 1.0 m$$

A Block Starts from Rest at the Top of a 31.0°