A horizontal pipe CD freely rotates about an axis AB. A small ball with mass m is

initially put inside the pipe at M (MC = a). Given the pipe an initial rotation rate of coo.

determine when the ball reaches the exit D (1) the small ball's rotation rate, ∞, and (2) the

force the pipe acting on the ball at D. Free-body diagram is required.

 

A uniform steel beam AB of Weight  is loaded as indicated in the Figure 1 below:

Figure 1.

It is required to determine:

1. The magnitude of the reactions and , in the absence of the external force F.

1. the magnitude of the load F acting at B that makes the reaction force at A to be zero.

1. the magnitude of when F is acting at B.

3. Explain why, for a gas, the specific heat at constant volume has a different value 
from the specific heat at constant pressure.
An ideal gas is contained in a cylinder fitted with a piston. Initially the temperature of the 
gas is 15℃. If the mass of the gas is 0.035 kg, calculate the quantity of heat energy 
required to raise the temperature of the gas to 150 ℃ when:
(a) The piston is fixed;
(b) The piston moves and the pressure is constant.
For the gas, 𝑐𝑣 = 676 J/kg-K and 𝑐𝑝 = 925 J/kg-K.

1. Calculate the quantity of heat energy which must be transferred to 2.25 kg of brass to 
raise its temperature from 20 ℃ to 240 ℃ if the specific heat of brass is 394 J.kg-K.

2. Find the change in temperature produced by 10 kJ of heat energy added to 500 g 
copper. Specific heat of copper 0.39 kJ/kg-K.

3. Explain why, for a gas, the specific heat at constant volume has a different value 
from the specific heat at constant pressure.
An ideal gas is contained in a cylinder fitted with a piston. Initially the temperature of the 
gas is 15℃. If the mass of the gas is 0.035 kg, calculate the quantity of heat energy 
required to raise the temperature of the gas to 150 ℃ when:
(a) The piston is fixed;
(b) The piston moves and the pressure is constant.
For the gas, 𝑐𝑣 = 676 J/kg-K and 𝑐𝑝 = 925 J/kg-K.