How Is the Spring Constant Calculated from Block Compression and Friction?

AI Thread Summary
To calculate the spring constant from the block's compression and friction, the kinetic energy (Ek) of the block is first determined using the formula Ek = 1/2 mv^2, resulting in 3.6 J. The frictional force is calculated using Ff = μFn, where the normal force (Fn) equals the gravitational force due to the block's mass on a horizontal surface. The energy lost to friction must be accounted for in the total energy equation, which combines the kinetic energy and the potential energy stored in the spring (Ep = 1/2 kx^2). By equating the energy lost to friction and the potential energy of the spring, the spring constant (k) can be solved. Understanding these relationships is crucial for accurately calculating the spring constant in this scenario.
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Homework Statement


A 1.8kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 2.0m/s and compresses it a distance of 0.11m before coming to rest. The coefficent of friction between the block and the surface is 0.560. What is the force constant of the spring?


Homework Equations


Ep=1/2kx^2
Ek=1/2mv^2


The Attempt at a Solution


I used Ek=1/2mv^2 to find Ek and I got 3.6J. I can use Ff=uFn to find force friction, but I don't know what to do? help.
 
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Since you know the mass of the object you would also know the Force of Gravity. Since force of gravity = Normal Force whenever its perfectly horizontal, then you could use that number you got times mew to get your frictional force
 

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