Answer:
a) the impulse exerted by the rivet when the anvil has an infinite mass support is 0.932 lb.s
the energy absorbed by the rivet under each blow when the anvil has an infinite mass support = 9.32 ft.lb
b) the impulse exerted by the rivet when the anvil has a support weight of 9 lb = 0.799 lb.s
the energy absorbed by the rivet under each blow when the anvil has a support weight of 9 lb is = 7.99 ft.lb
Explanation:
The first picture shows a schematic view of a free body momentum diagram of the hammer head and the anvil.
Using the principle of conservation of momentum to determine the final velocity of anvil and hammer after the impact; we have:
From the question given, we can deduce that the anvil is at rest;
∴ ; then, we have:
Making the subject of the formula; we have:
------- Equation (1)
Also, from the second diagram; there is a representation of a free body momentum of the hammer head;
From the diagram;
F = impulsive force exerted on the rivet
Δt = the change in time of application of the impulsive force
Using the principle of impulse of momentum to the hammer in the quest to determine the impulse exerted (i.e FΔt ) on the rivet; we have:
------- Equation (2)
Using the function of the kinetic energy of the hammer before impact ; we have:
-------- Equation (3)
We determine the mass of the hammer by using the formula from:
where;
= weight of the hammer
= mass of the hammer
g = acceleration due to gravity
Making the subject of the formula; we have:
Now;
After the impact ; the final kinetic energy of the hammer and anvil can be written as:
Recall from equation (1) ; where ; if we slot that into the above equation; we have:
Also; from equation (3)
; Therefore;
----- Equation (4)
a)
Now; To calculate the impulse exerted by the rivet FΔt and the energy absorbed by the rivet under each blow ΔT when the anvil has an infinite mass support; we have the following process
First , we need to find the mass of the anvil when we have an infinite mass support;
mass of the anvil
where we replace; and g = 32.2 ft/s²
However ; from equation (1)
From equation (2)
Therefore the impulse exerted by the rivet when the anvil has an infinite mass support is 0.932 lb.s
For the energy absorbed by the rivet ; we have:
where;
Then;
Then the energy absorbed by the rivet under each blow ΔT when the anvil has an infinite mass support
ΔT =
ΔT = 9.316 ft.lb - 0
ΔT ≅ 9.32 ft.lb
Therefore; we conclude that the energy absorbed by the rivet under each blow when the anvil has an infinite mass support = 9.32 ft.lb
b)
Due to the broadness of this question, the text is more than 5000 characters, so i was unable to submit it after typing it . In the bid to curb that ; i create a document for the answer for the part b of this question.
The attached file can be found below.
