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I finished with my first semester of physics in Spring, and I thought that I had understood the unit on springs pretty well; however, today a friend gave me this problem to solve, and I’m drawing such a massive blank, it’s not even funny. I’m so frustrated with this problem.
The diagram is drawn as follows: there are five masses (from left to right: M1, M2, M3, M4, M5) connected to each other by springs, resting on a horizontal surface. M1 = 2kg, M2 = 2kg, M3 = 3kg, M4 = 3kg, M5 = 5kg. Between M1 & M2, the speed of the force is 100 N/m; between M2 & M3, the speed of the force is 200 N/m; between M3 & M4, the speed is 200 N/m; between M4 & M5, the speed is 200 N/m. The force is being applied to M5 [furthest right], direction left.
The problem:
Fnet = ma = 0
Ffriction = mu*Fnormal = mu*abs(Fgrav)
Fspring = kx, where x = displacement of spring from equilibrium
What does N/m mean with regards to springs? Is that how much force is transferred to the block next in line in the springmass system? Am I to use that relationship to find out what x is? But I don’t even know k. Do I? I’m setting the origin at M5, with the left direction as negative.
If I’m pushing on M5, the horizontal net force is Fnethorizontal = 90 N + Ffriction = 90 N + mu*abs(Fgravity) = 90 N + 0.1*abs(5*9.8) = 85.1 N
So then what? Substitute 85.1 N in to the relationship 200 N/m to solve for m? If I do, I end up with 0.4225 m. Then, using 85.1 N and 0.4225 m, do I substitute that in to find the value of the spring constant? Because it doesn’t look right at all. I come up with k being 201.4 ...
But why am I even finding the spring constant? I feel like I’m sort of really lost, and like I don’t understand springs at all. @_@;; I looked through my book, and again, massive blank.
Homework Statement
The diagram is drawn as follows: there are five masses (from left to right: M1, M2, M3, M4, M5) connected to each other by springs, resting on a horizontal surface. M1 = 2kg, M2 = 2kg, M3 = 3kg, M4 = 3kg, M5 = 5kg. Between M1 & M2, the speed of the force is 100 N/m; between M2 & M3, the speed of the force is 200 N/m; between M3 & M4, the speed is 200 N/m; between M4 & M5, the speed is 200 N/m. The force is being applied to M5 [furthest right], direction left.
The problem:
An external force of magnitude 90 N is applied to a system of blocks connected by springs. After some time the system will move as a whole with constant acceleration. Find this acceleration. The coefficient of kinetic friction between the surface & the blocks is mukinetic = 0.1...
Homework Equations
Fnet = ma = 0
Ffriction = mu*Fnormal = mu*abs(Fgrav)
Fspring = kx, where x = displacement of spring from equilibrium
The Attempt at a Solution
What does N/m mean with regards to springs? Is that how much force is transferred to the block next in line in the springmass system? Am I to use that relationship to find out what x is? But I don’t even know k. Do I? I’m setting the origin at M5, with the left direction as negative.
If I’m pushing on M5, the horizontal net force is Fnethorizontal = 90 N + Ffriction = 90 N + mu*abs(Fgravity) = 90 N + 0.1*abs(5*9.8) = 85.1 N
So then what? Substitute 85.1 N in to the relationship 200 N/m to solve for m? If I do, I end up with 0.4225 m. Then, using 85.1 N and 0.4225 m, do I substitute that in to find the value of the spring constant? Because it doesn’t look right at all. I come up with k being 201.4 ...
But why am I even finding the spring constant? I feel like I’m sort of really lost, and like I don’t understand springs at all. @_@;; I looked through my book, and again, massive blank.
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