1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pogonyaev
3 years ago
15

. Two rods, with masses MA and MB having a coefficient of restitution, e, move

Engineering
1 answer:
GarryVolchara [31]3 years ago
7 0

Answer:

a) V_A = \frac{(M_A - eM_B)U_A + M_BU_B(1+e)}{M_A + M_B}

V_B = \frac{M_AU_A(1+e) + (M_B - eM_A)U_B}{M_A + M_B}

b) U_A = 3.66 m/s

V_B = 4.32 m/s

c) Impulse = 0 kg m/s²

d) percent decrease in kinetic energy = 47.85%

Explanation:

Let U_A be the initial velocity of rod A

Let U_B be the initial velocity of rod B

Let V_A be the final velocity of rod A

Let V_B be the final velocity of rod B

Using the principle of conservation of momentum:

M_AU_A + M_BU_B = M_AV_A + M_BV_B............(1)

Coefficient of restitution, e = \frac{V_B - V_A}{U_A - U_B}

V_A = V_B - e(U_A - U_B)........................(2)

Substitute equation (2) into equation (1)

M_AU_A + M_BU_B = M_A(V_B - e(U_A - U_B)) + M_BV_B..............(3)

Solving for V_B in equation (3) above:

V_B = \frac{M_AU_A(1+e) + (M_B - eM_A)U_B}{M_A + M_B}....................(4)

From equation (2):

V_B = V_A + e(U_A -U_B)......(5)

Substitute equation (5) into (1)

M_AU_A + M_BU_B = M_AV_A + M_B(V_A + e(U_A -U_B))..........(6)

Solving for V_A in equation (6) above:

V_A = \frac{(M_A - eM_B)U_A + M_BU_B(1+e)}{M_A + M_B}.........(7)

b)

M_A = 2 kg\\M_B = 1 kg\\U_B = -3 m/s( negative x-axis)\\e = 0.65\\U_A = ?

Rod A is said to be at rest after the impact, V_A = 0 m/s

Substitute these parameters into equation (7)

0 = \frac{(2 - 0.65*1)U_A - (1*3)(1+0.65)}{2+1}\\U_A = 3.66 m/s

To calculate the final velocity, V_B, substitute the given parameters into (4):

V_B = \frac{(2*3.66)(1+0.65) - (1 - (0.65*2))*3}{2+1}\\V_B = 4.32 m/s

c) Impulse, I = M_AV_A + M_BV_B - (M_AU_A + M_BU_B)

I = (2*0) + (1*4.32) - ((2*3.66) + (1*-3))

I = 0 kg m/s^2

d) %\triangle KE = \frac{(0.5 M_A V_A^2 + 0.5 M_B V_B^2) - ( 0.5 M_A U_A^2 + 0.5 M_B U_B^2)}{0.5 M_A U_A^2 + 0.5 M_B U_B^2} * 100\%

%\triangle KE = \frac{((0.5*2*0) + (0.5 *1*4.32^2)) - ( (0.5 *2*3.66^2) + 0.5*1*(-3)^2))}{ (0.5 *2*3.66^2) + 0.5*1*(-3)^2)} * 100\%

% \triangle KE = -47.85 \%

You might be interested in
What are the two reasons for a clear cut
Inessa [10]

Answer:

to clear land for agriculture and settlement and to use or sell timber for lumber, paper products, or fuel.

3 0
2 years ago
Steam enters an adiabatic turbine at 400◦C, 2 MPa pressure. The turbine has an isentropic efficiency of 0.9. The exit pressure i
pychu [463]

Answer:

Explanation:

Find attached the solution

8 0
2 years ago
________ are written to “maximize” or “minimize” a specific value associated with the product needs in order to define the goal
Anna35 [415]

Answer:

Objective statements.

Explanation:

An objective statement can be defined as a short statement that explicitly states or describes what a person wants exactly or is looking out for in a particular item.

Objective statements are written to “maximize” or “minimize” a specific value associated with the product needs in order to define the goal or aim of the design process.

This ultimately implies that, objective statements are used by various manufacturing industries or companies to explicitly define the minimum or maximum requirements for the production of its goods.

4 0
3 years ago
Read 2 more answers
As cylinder pressure and heat increase due to an increased load condition, the fuel injection management system must ___________
Temka [501]

possible Answers:

Compensate ⭐⭐⭐⭐⭐

Adjust            ⭐⭐⭐⭐⭐

regulate         ⭐⭐⭐⭐

tune               ⭐⭐⭐

calibrate        ⭐⭐⭐

balance         ⭐⭐

correct           ⭐

6 0
2 years ago
Statement true about fats in food
Elodia [21]

Answer:

What that means please explain

7 0
2 years ago
Read 2 more answers
Other questions:
  • 1. Computers are fully digital which means: A. They can’t convert things from analog B. They work only with numeric digits (base
    6·1 answer
  • A fluid flows steadily through a pipe with a uniform cross sectional area. The density of the fluid decreases to half its initia
    6·1 answer
  • At the instant shown, slider block B is moving with a constant acceleration, and its speed is 150 mm/s. Knowing that after slide
    13·1 answer
  • The water requirement for Class H cement is 38% (i.e.,water (%) by weight of cement),whereas the water requirement for barite is
    7·1 answer
  • A stem and leaf display
    12·1 answer
  • An aquifer has three different formations. Formation A has a thickness of 8.0 m and hydraulic conductivity of 25.0 m/d. Formatio
    9·1 answer
  • Which option identifies the step of the implementation phase represented in the following scenario?
    9·2 answers
  • Can someone explain the answer for this question please? -metrology
    12·1 answer
  • Guess the output of this code: print( (3**2)//2)​
    13·1 answer
  • Re armature of a 4 pole DC generator is required to generate an emf of 520v on open circuit when revolving at a speed of 660rpm.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!