Given:
Ca = 3Cb (1)
where
Ca = heat capacity of object A
Cb = heat capacity f object B
Also,
Ta = 2Tb (2)
where
Ta = initial temperature of object A
Tb = initial temperature of object B.
Let
Tf = final equilibrium temperature of both objects,
Ma = mass of object A,
Mb = mass of object B.
Assuming that all heat exchange occurs exclusively between the two objects, then energy balance requires that
Ma*Ca*(Ta - Tf) = Mb*Cb*(Tf - Tb) (3)
Substitute (1) and (2) into (3).
Ma*(3Cb)*(2Tb - Tf) = Mb*Cb*(Tf - Tb)
3(Ma/Mb)*(2Tb - Tf) = Tf - Tb
Define k = Ma/Mb, the ratio f the masses.
Then
3k(2Tb - Tf) = Tf - Tb
Tf(1+3k) = Tb(1+6k)
Tf = [(1+6k)/(1+3k)]*Tb
Answer:

where
Answer:
we have to find out the critical resolved shear stress. As it it given in the question
Ф = 28.1°and the possible values for λ are 62.4°, 72.0° and 81.1°.
a) Slip will occur in the direction where cosФ cosλ are maximum. Cosine for all possible λ values are given as follows.
cos(62.4°) = 0.46
cos(72.0°) = 0.31
cos(81.1°) = 0.15
Thus, the slip direction is at the angle of 62.4° along the tensile axis.
b) now the critical resolved shear stress can be find out by the following equation.
τ
= σ
( cosФ cosλ)
now by putting values,
= (1.95MPa)[ cos(28.1) cos(62.4)] = 0.80 MPa (114 Psi) 7.23
1) Yes
2) 
Explanation:
1)
To solve this part, we have to calculate the pressure at the depth of the batyscaphe, and compare it with the maximum pressure that it can withstand.
The pressure exerted by a column of fluid of height h is:

where
is the atmospheric pressure
is the fluid density
is the acceleration due to gravity
h is the height of the column of fluid
Here we have:
is the sea water density
h = 5440 m is the depth at which the bathyscaphe is located
Therefore, the pressure on it is

Since the maximum pressure it can withstand is 60 MPa, then yes, the bathyscaphe can withstand it.
2)
Here we want to find the force exerted on the bathyscaphe.
The relationship between force and pressure on a surface is:

where
p is hte pressure
F is the force
A is the area of the surface
Here we have:
is the pressure exerted
The bathyscaphe has a spherical surface of radius
r = 3 m
So its surface is:

Therefore, we can find the force exerted on it by re-arranging the previous equation:

Answer:
(a) The magnitude of the lift force is 52144.71 N, approximately.
(b) The magnitude of the air resistance force opposing the movement is 17834.54 N, approximately.
Explanation:
Since the helicopter is moving horizontally at a constant velocity, we can assume that the net force acting on it is zero, then
(a) in the vertical direction we have
.
(b) Now horizontally,
Momentum of elephant = 6300 * 0.11 = 693 kg-m/s
Momentum for the dolphin = 50 * 10.4 = 520 kg-m/s
Difference in momentum = 693 - 520 = 173 kg-m/s