a)Suppose the spring of part a ( k = 2350 N/m) is still attached to mass m = 329

Question

a)Suppose the spring of part a (k = 2350 N/m) is still attached to mass m = 329 g on a horizontal table. The spring is stretched distance x = 8.92 cm, and released from rest. Find v, the speed of the mass as it passes through the equilibrium position.
? m/s

b)A vertical rope is used to lower a block of mass M = 23.5 kg at a constant acceleration of magnitude a = 4.73 m/s2. Find WT, the work done by the tension in the cord if the mass moves down distance s = 2.8 m.
? J

c)Joe, mass MJ = 77.2 kg, is racing against Tom. When Joe and Tom have the same kinetic energy, Tom is running faster. When Joe increases his speed by 24.7%, they are running at the same speed. Find Tom's mass.
? Kg

d)A 200 W bulb works for time t = 6.29 hours. How many bricks of mass m = 167 g can be lifted to the top of building of height H = 80.9 m with this energy?
? bricks

<<PLEASE EXPLAIN STEP BY STEP>>

Explanation / Answer

a)0.5mv^2 = 0.5kx^2 => 0.329*v^2 = 2350*0.0892^2 => v = 7.539 m/s b)T-mg = -ma => T = m(g-a) = 23.5*(9.8-4.73) = 119.145 N work done = T*-x = -119.145*2.8 = 333.606 J c)0.5MjVj^2 = 0.5MtVt^2 ---------------(1) 1.247Vj = Vt -----------------------------(2) Vt/Vj = 1.247 -----------------------------(3) (1)/(2) => MjVj /1.247= MtVt Mj/1.247 = Mt(Vt/Vj) = Mt*1.247 (by (3)) Mt = Mj/1.247*1.247 = 77.2/1.555009 = 49.65 kg Ans d)total energy = 200*6.29*3600 = 4528.8 kJ energy for 1 brick = mgh = 0.167*9.8*80.9 = 132.401 J no. of bricks = total energy/energy for 1 brick = 4528800/132.401 = 34205.18 bricks

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