A block of mass m = 4.5 kg rests on a frictionless floor. It is attached to a sp

Question

A block of mass m = 4.5 kg rests on a frictionless floor. It is attached to a spring with a relaxed length L = 5 m. The spring has spring constant k = 15 N / m and is relaxed when hanging in the vertical position. The block is pulled d = 6 m to one side. In this problem, the block is always constrained to move on the floor (i.e. it never leaves the floor). By what amount is the spring extended? What is the potential energy stored in the spring? The block is released but is constrained to move horizontally on the frictionless floor. What is the maximum speed it attains? Let's change the problem a bit. When the spring is vertical (hence, unstretched), the block is given an initial speed equal to 1.7 times the speed found in part How far from the initial (unstretched) point does the block go along the floor before stopping? What is the magnitude of the acceleration of the block at this point (when the spring is stretched farthest)?

Explanation / Answer

a) The spring lenght with the block moved 3 m is v[3² + 4²] = 5 m The spring extension is ?x = 5 - 4 = 1 m b) The energy stored in the spring is 0.5*k*?x² c) The maximum speed is when all the stored energy is transferred to the block, which happens when the spring is at its relaxed length, so the KE of the block = stored spring energy 0.5*m*v² = 0.5*k*?x², v = ?x*v[k/m] d) Using energy conservation with v1 = 2*?x*v[/k/m] 0.5*m*v1² = 0.5*k*?x1² 4*?x²*k = k*?x1² ?x1 = 2*?x SInce ?x = 1 m, ?x1 = 2 m, The distance from the unstretched point is d = v[(4+2)² - 4²] = 4.47 m e) The horizontal force on the block is k*?x1*cos?. The acceleration is F/m = k*?x1*cos?/m. cos? = d/(4+2) help ful

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