What is the minimum spring compression delta necessary to cause m2 to leave the floor after m1 suddenly released with zero velocity? Measure delta from the unstretched length of the spring and assume that all the motion is in vertical direction
To determine the minimum spring compression delta (Δ) required for m2 to leave the floor after m1 is suddenly released with zero velocity, we need to consider the forces acting on the system.
Let's break down the steps to find out the answer:
Step 1: Identify the forces acting on the system
When m1 is released, both m1 and m2 experience the force of gravity acting downward (mg). Additionally, the spring exerts an upward force (Fs) due to its compression.
Step 2: Determine the equilibrium condition
In order for m2 to leave the floor, the net force acting on the system needs to be zero. This means that the gravitational force and the spring force must balance each other.
Step 3: Set up the equilibrium equation
The equilibrium equation is given by:
mg - Fs = 0
Step 4: Express gravitational force and spring force in terms of their variables
Using the equation above, we can express the gravitational force and the spring force as:
mg - kΔ = 0
where k is the spring constant and Δ is the compression of the spring.
Step 5: Solve for Δ
To find the minimum compression delta required for m2 to leave the floor, we set the gravitational force equal to the spring force and solve for Δ:
mg = kΔ
Δ = mg / k
Therefore, to find the minimum spring compression delta necessary for m2 to leave the floor, divide the product of m2 and the acceleration due to gravity (g) by the spring constant (k).