Answer:
a = 3.608 ft/s²
T = 5.977 kip
Explanation:
Angle of inclined track is not given. It is 5 degree as shown in attached image 1.
Given data:
Weight of boxcar A = Wα = 20,000 lb
Weight of boxcar B = Wb = 30,000 lb
Coefficient of kinetic friction = υk = 0.5
angle of inclined track = 5 degree
Value of g = 32.2 ft/s²
Solution:
These boxcars are moving therefore,
∑Fₓ = ma
∑
Car A
Use ∑
Forces acting in Y-axis are weight and its counter N (as shown in Free body diagram). Weight is Negative (acting downward) while N is positive (acting upward)
∑ Nα - Wα*Cos(∅) = 0
∑ Nα - 20,000*Cos(5°) = 0
∑ Nα - 20,000*0.9962 = 0
∑ Nα - 19,924 = 0
Nα = 19,924
Use ∑Fₓ = maₓ
Forces acting in x-axis are Fa, T and horizontal component of weight and force having acceleration a (as shown in Free body diagram). Horizontal component of weight and Tension (T) are Negative (acting in negative X-axis direction) while Fa is positive (acting in positive X-axis direction)
∑Fₓ = maₓ
(0.5*19924) - 20,000*Sin(5°) - T = (20,000/32.2)*a
9962 - 1744 - T = 621.12*a
8218 - T = 621.12*a .................. Eq(1)
Both cars
∑Fₓ = maₓ
Forces acting are; horizontal component of weights, Fa and force having acceleration a (as shown in Free body diagram).
9962 - 1744 - 2616 = 621.12/a + 931.68/a
5602 = 1552.8 / a
⇒ a = 3.608 ft/s²
put a = 3.608 ft/s² in equation (1)
⇒ T = 8218 - 621.12*3.608
T = 8218 - 2240.79
T = 5977.21 lb
T = 5.977 kip
Answer:
a) Under damped
Explanation:
Given that system is critically damped .And we have to find out the condition when gain is increased.
As we know that damping ratio given as follows
Where C is the damping coefficient and Cc is the critical damping coefficient.
So from above we can say that
From above relationship we can say when gain (K) is increases then system will become under damped system.
To solve this problem we will apply the concepts related to translational torque, angular torque and the kinematic equations of angular movement with which we will find the angular displacement of the system.
Translational torque can be defined as,
Here,
F = Force
d = Distance which the force is applied
At the same time the angular torque is defined as the product between the moment of inertia and the angular acceleration, so using the previous value of the found torque, and with the moment of inertia given by the statement, we would have that the angular acceleration is
Now the angular displacement is
Here
= Initial angular velocity
t = time
Angular acceleration
= Angular displacement
Time is given as 1 minute, in seconds will be
There is not initial angular velocity, then
Replacing,
The question neglects the effect of gravitational force.
Answer:
No.
Explanation:
The Coefficient of Performance of the reversible heat pump is determined by the Carnot's cycle:
The power required to make the heat pump working is:
The heat absorbed from the exterior air is:
According to the Second Law of Thermodynamics, the entropy generation rate in a reversible cycle must be zero. The formula for the heat pump is:
Which contradicts the reversibility criterion according to the Second Law of Thermodynamics.