Two rods, with masses MA and MB having a coefficient of restitution, e, move along a common line on a surface, figure 2. a) Find
the general expression for the velocities of the two rods after impact. b) If mA = 2 kg, m3 = 1 kg, Vo= 3 m/s, and e = 0.65, find the value of the initial velocity v4 of rod A for it to be at rest after the impact and the final velocity vB of rod B. c) Find the magnitude of the impulse for the condition in part b. (3 marks) d) Find the percent decrease in kinetic energy which corresponds to the impact in part b.
1 answer:
Answer:
A.) Find the answer in the explanation
B.) Ua = 7.33 m/s , Vb = 7.73 m/s
C.) Impulse = 17.6 Ns
D.) 49%
Explanation:
Let Ua = initial velocity of the rod A
Ub = initial velocity of the rod B
Va = final velocity of the rod A
Vb = final velocity of the rod B
Ma = mass of rod A
Mb = mass of rod B
Given that
Ma = 2kg
Mb = 1kg
Ub = 3 m/s
Va = 0
e = restitution coefficient = 0.65
The general expression for the velocities of the two rods after impact will be achieved by considering the conservation of linear momentum.
Please find the attached files for the solution
You might be interested in
Answer:
1.287 *10⁷ cycles.
Explanation:
See attached pictures.
Answer:
the endurance strength = 421.24 MPa
Explanation:
From the given information; The objective is to estimate the endurance strength, Se, in MPa .
To do that; let's for see the expression that shows the relationship between the ultimate tensile strength and Brinell hardness number .
It is expressed as:
where;
= Brinell hardness number
= Ultimate tensile strength
From ;
; replace 290 for
; we have
988.9 MPa
We can see that the derived value for the ultimate tensile strength when the Brinell harness number = 290 is less than 1400 MPa ( i.e it is 988.9 MPa)
So; we can say
The Endurance limit can be represented by the formula:
= 494.45 MPa
Using Table 6.2 for parameter for Marin Surface modification factor. The value for a and b are derived; which are :
a = 1.58
b = -0.085
The value of the surface factor can be calculate by using the equation
The formula that is used to determine the value of for the rotating shaft of size factor d = 10 mm is as follows:
Finally; the the endurance strength, Se, in MPa if the rod is used in rotating bending is determined by using the expression;
= 0.8792×0.969×494.45
= 421.24 MPa
Thus; the endurance strength = 421.24 MPa