One end of a spring is attached firmly to a wall, and a block is attached to the other end. When the spring is fully compressed, it exerts a force F on the block, and when the spring is fully extended, the force it exerts on the block is −F. What is the force of the spring on the block at (a) equilibrium (neither compressed nor stretched), (b) halfway between maximum stretch and equilibrium, and (c) halfway between maximum compression and equilibrium? Carefully consider the signs in your answer, which indicate direction, and express your answers in terms of F.
Please, help.
Thank you.
A) 0
B) .5
C)-.5
To find the force of the spring on the block at different positions, we can refer to Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Let's consider the different positions of the block and calculate the force exerted by the spring:
(a) At equilibrium (neither compressed nor stretched), the displacement of the spring from its equilibrium position is zero. According to Hooke's Law, when there is no displacement, the force exerted by the spring is also zero. Therefore, the force of the spring on the block at equilibrium is 0F or simply 0.
(b) Halfway between maximum stretch and equilibrium: In this case, let's assume the maximum displacement of the spring is represented by "d". Halfway between maximum stretch and equilibrium, the displacement of the spring is "d/2" (half of the maximum).
According to Hooke's Law, the force exerted by the spring is directly proportional to the displacement. Therefore, halfway between maximum stretch and equilibrium, the force of the spring on the block would be halfway between maximum force and 0 force.
Since the maximum force is F and the 0 force is −F, we can calculate the halfway force as follows:
Halfway force = (0 force + maximum force) / 2 = (-F + F) / 2 = 0F / 2 = 0
Therefore, at halfway between maximum stretch and equilibrium, the force of the spring on the block is 0F.
(c) Halfway between maximum compression and equilibrium: Similar to the previous case, when the displacement of the spring is "d/2" (half of the maximum compression), the force of the spring on the block would also be halfway between the maximum force and 0 force.
Using the same calculation as in the previous case, we find that at halfway between maximum compression and equilibrium, the force of the spring on the block is 0F.
In summary:
(a) At equilibrium: 0F
(b) Halfway between maximum stretch and equilibrium: 0F
(c) Halfway between maximum compression and equilibrium: 0F
Therefore, regardless of the position, the force of the spring on the block is always 0F.