unknown mass mass 1 in water igure 1: Diagram showing the physical set-up for pr

Question

unknown mass mass 1 in water igure 1: Diagram showing the physical set-up for problem 2. ll strings and pulleys are masles and ulleys are frictionless. (2) In Figure 1, is an atwood machine with one mass, mass 1, in a container of water. Mass 1 has a mass of 150 g and a volume of 35.0 cm. (10 points) (a) What must the unknown mass be to keep mass 1 neutrally bouyant, completely submerged, but not moving? (5 points) (b) If the unknown mass is set at 200 g, what is the acccleration of mass 1 while it is still in the water? (5 points) /A

Explanation / Answer

a) let unknown mass 2 = m

=> tension in cable = T = mg

bouyant force, Fb = volume displaced*density of water*g = 35 cm^3 *10^-3* 1g/cm^3 *9.8 = 0.343 N

and weight of mass 1 = m1*g = 0.15*9.8 = 1.47 N

for neutrally balance

T + Fb = 1.47

=> mg + 0.343 = 1.47

=> m = 115 gram

b) if m = 200 gram

then T + Fb - m1g = m1*a

=> 0.200*9.8 + 0.343 - 0.15*9.8 = 0.15*a

=> acceleration , a = 5.55 m/s^2 upward

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