A block of metal is placed on top of a half-sphere made of ice. The block slides

Question

A block of metal is placed on top of a half-sphere made of ice. The block slides on the half-sphere down to a height h above the ground, then it loses contact with the ice surface and falls to the The half-sphere has a radius R = 2 m: can ignore the friction between the ice and the metal. a) What is the force exerted by the half-sphere on the block at the moment in which the block contact with the ice? b) Calculate h. An Atwood machine consists of two masses m_A = 6.3 kg and m_B = 7.9 kg, connected by a that passes over a pulley free to rotate about a fixed axis. The pulley is a solid cylinder of radius R_B = 0.30 m and mass M = 0.40 kg. The moment of inertia of the pulley with respect to an axis around which the pulley is rotating in this problem is J = MR^2_0/2. a) Draw the free body diagram for each of the two masses for the pulley. b) Calculate the acceleration (magnitude and direction) of the weights. An amount of heat Q = 43.7 kJ is absorbed from = 0.333 kg of water at T = 0C degree. Part of the water freezes and turns into ice. What is the mass of the remaining water? The heat of fusion for water is One mole of an ideal gas expands isothermally. The initial volume occupied by the gas is the final volume if and the temperature of the gas is T = 25 C degree. Calculate the heat absorbed by the gas during the expansion. The ideal gas constant is R = 8.314 J/(mol K).

Explanation / Answer

According to first law of thermodynamics,

U = Q - Wsys

For isothermal process, U = 0. So,

Q = Wsys = PdV

For ideal gas, P = nRT/V. So,

Q = nRT ViVf dV/V

=> Q = nRT [lnV]ViVf

=> Q = nRT ln(Vf / Vi)

=> Heat absorbed, Q = 1 * 8.314 * (273 + 25) * ln(3 / 1.5) = 1717.3 J

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