Answer:
The true stress at true strain 0.05cm/cm is 80MPa
Explanation:
Given that
the strength coefficient is K
true strain is ε
strain hardening exponent is n
initial diameter of bar is d = 1cm, (10mm)
tensile force is F
engineering stress(S) = 120
the engineering stress(S) =
To find force (F) =
120 =
F = 120 * (π/4) * (100)
F = 9425N
Calculate the true strain (ε) = In (l₀ / l₁)
where
l₀ = initial length of the metallic bar = 3cm
l₁ = final length of metallic bar = 3.5cm
ε = In (3.5 / 3)
= In 1.1667
= 0.154cm/cm
Calculate the true stress (σ) at fracture point
=
tensile force is F and final diameter of bar is d₁ (d in the eqn)
Substitute 9425 N for F and 0.926 cm (9.26mm) for d₁ (d in the eqn)
σ =
= 140MPa
To find the strength coefficient (K) of the material bar
K =
K =
= 356.75MPa
To calculate the true stress σ true strain of 0.05cm/cm
K = 356.75MPa
σ =
=
= 80MPa
The true stress at true strain 0.05cm/cm is 80MPa
Answer:
Mechanical advantage = 2.875
Explanation:
Given:
A diagram is shown below for the above scenario.
Length of ramp (Effort arm) = 4.6 m
Height of truck bed ( Resistance length) = 1.6 m
Mechanical advantage (MA) is the ratio of effort arm and resistance length.
So, mechanical advantage is given as,
(a) Zero
When the ball reaches its highest point, the direction of motion of the ball reverses (from upward to downward). This means that the velocity is changing sign: this also means that at that moment, the velocity must be zero.
This can be also understood in terms of conservation of energy: when the ball is tossed up, initially it has kinetic energy
where m is the ball's mass and v is the initial speed. As it goes up, this kinetic energy is converted into potential energy, and when the ball reaches the highest point, all the kinetic energy has been converted into potential energy:
where g is the gravitational acceleration and h is the height of the ball at highest point. At that point, therefore, the potential energy is maximum, while the kinetic energy is zero, and so the velocity is also zero.
(b) 9.8 m/s upward
We can find the velocity of the ball 1 s before reaching its highest point by using the equation:
where
a = g = -9.8 m/s^2 is the acceleration due to gravity, which is negative since it points downward
v = 0 is the final velocity (at the highest point)
u is the initial velocity
t = 1 s is the time interval
Solving for u, we find
and the positive sign means it points upward.
(c) -9.8 m/s
The change in velocity during the 1-s interval is given by
where
v = 0 is the final velocity (at the highest point)
u = 9.8 m/s is the initial velocity
Substituting, we find
(d) 9.8 m/s downward
We can find the velocity of the ball 1 s after reaching its highest point by using again the equation:
where this time we have
a = g = -9.8 m/s^2 is the acceleration due to gravity, still negative
v is the final velocity (1 s after reaching the highest point)
u = 0 is the initial velocity (at the highest point)
t = 1 s is the time interval
Solving for v, we find
and the negative sign means it points downward.
(e) -9.8 m/s
The change in velocity during the 1-s interval is given by
where here we have
v = -9.8 m/s is the final velocity (1 s after reaching the highest point)
u = 0 is the initial velocity (at the highest point)
Substituting, we find
(f) -19.6 m/s
The change in velocity during the overall 2-s interval is given by
where in this case we have:
v = -9.8 m/s is the final velocity (1 s after reaching the highest point)
u = +9.8 m/s is the initial velocity (1 s before reaching the highest point)
Substituting, we find
(g) -9.8 m/s^2
There is always one force acting on the ball during the motion: the force of gravity, which is given by
where
m is the mass of the ball
g = -9.8 m/s^2 is the acceleration due to gravity
According to Newton's second law, the resultant of the forces acting on the body is equal to the product of mass and acceleration (a), so
which means that the acceleration is
and the negative sign means it points downward.