Two blocks are connected by a string that passes over a massless, frictionless p

Question

Two blocks are connected by a string that passes over a massless, frictionless pulley, as shown in the figure. Block A, with a mass mA- 3.00 kg, rests on a ramp measuring 3.0 m vertically and 4.0 m horizontally. Block B hangs vertically below the pulley. Note that you can solve this exercise entirely using forces and the constant-acceleration equations, but see if you can apply energy ideas instead. Use g 10 m/s2. When the system is released from rest, block A accelerates up the slope and block B accelerates straight down. When block B has fallen through a height h2.0 m, its speed is v 4.00 m/s that you can solve this A 3.0m -4.0 m-+ (a) Assuming that no friction is acting on block A, what is the mass of block B? 5.11 x kg (b) If, instead, there is friction acting on block A, with a coefficient of kinetic friction of 5/8, what is the mass of block B? kg

Explanation / Answer

a] By third equation of motion, a = v^2/2s = 4^2/(2*2) = 4 m/s^2

Tension T = mA a + mA g *3/5

= 3*4 + 3*10*3/5 = 30 N,

mBg - T = mB a

10mB = T+ 4mB

6 mB = 30

mB = 5 kg answer

b] Tension T = mA a + mA g *3/5 + u mA g *4/5

= 3*4 +  3*10*3/5+ 5/8*3*10*4/5 = 45 N

mBg - T = mB a

10mB = T+ 4mB

6 mB = 45

mB = 7.5 kg answer

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