\"A tank of water sits on a cart with frictionless wheels as shown. The cart is

Question

"A tank of water sits on a cart with frictionless wheels as shown. The cart is attached using a cable to a mass M=10 kg, and the coefficient of static friction of the mass with the ground is s= 0.55. If the gate blocking the tank exit is removed, will the resulting exit flow be sufficient to start the tank moving? (Assuming the water flow is frictionless, and that the jet velocity is V=2gh, where h = 2m is the water depth. Find the mass M that is just sufficient to hold the tank in place." The exit tube has and angle of  = 60o with a diameter of 50mm.

Explanation / Answer

If use M=10kg (not 9kg shown in the figure) and h=2m (not 4m shown in the figure)

V=2gh = 6.264 m/s

horizontal component of force from water jet = AV(Vcos60)

= 1000*/4*(0.042)*6.264*(6.264*0.5) = 24.66 N

Force required to overcome static friction = 0.55*10*9.81 =53.96 N > force from water jet

Therefore --> The tank+cart will not move

The mass M that is just sufficient to hold the tank in place

0.55*9.81*M = 24.66

M = 4.57 kg

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