a) Calculate the P.E. a pile driver has if it is raised 4.5 meters by a mechanical winch. If the 510
kilogram pile driver is allowed to fall freely, what would its velocity be at ground level.
b) A 4.2 kg mortar shell is fired out of a mortar with a velocity of 120 m/s. What is the kinetic
energy of the shell at this instant?
c) In a stamping machine the die has a mass of 35 kg and falls from a height of 2 m onto a metal block. If the depth of indentation is 10 mm find the average stamping force assuming
the die does not rebound.
please provide full answers much appreciated!
a/ V=√2gh
V=√(2×9.8×4.5)
V=9.39
b/=> K.E= (mv^2)/2
=> K.E= (4.2 ×〖120〗^2)/2
=> K.E= 30240 J
=> K.E= 30.2kJ
c/
average force= (35×9.8×2)/0.01
ave.f=68600N
Ave.f= 68.6 KN
a is 9.39m/s, b is 30.2kJ, c is 68.6KN
omg noob!!!! That's not how you solve it!!!!!! I want working out too!!!!!!!!!!!!!!!
ayy lmao
V=√2gh
V=√(2×9.8×4.5)
V=9.39 m/s
a) To calculate the potential energy (P.E.) of a pile driver raised by a mechanical winch, we can use the formula:
P.E. = mgh
where:
m = mass of the pile driver (510 kg)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height raised by the mechanical winch (4.5 m)
Substituting the values into the formula:
P.E. = (510 kg) × (9.8 m/s²) × (4.5 m)
P.E. = 22,302 Joules (rounded to the nearest whole number)
To find the velocity of the pile driver at ground level when it falls freely, we can use the law of conservation of energy. The potential energy at the initial height will be fully converted into kinetic energy at ground level.
Potential energy (P.E.) = Kinetic energy (K.E.)
Thus, we can equate the formulas:
mgh = (1/2)mv²
Simplifying the equation:
gh = (1/2)v²
Rearranging the equation for velocity (v):
v = √[2gh]
Substituting the values:
v = √[2 × 9.8 m/s² × 4.5 m]
v = √[88.2] m/s
v ≈ 9.4 m/s (rounded to one decimal place)
b) The kinetic energy (K.E.) of the mortar shell can be calculated using the formula:
K.E. = (1/2)mv²
where:
m = mass of the mortar shell (4.2 kg)
v = velocity of the mortar shell (120 m/s)
Substituting the values into the formula:
K.E. = (1/2) × (4.2 kg) × (120 m/s)²
K.E. = 30,240 Joules
The kinetic energy of the shell at that instant is 30,240 Joules.
c) To find the average stamping force in the stamping machine, we need to calculate the work done. The work done (W) is equal to the force (F) multiplied by the displacement (d).
W = F × d
Given that the mass of the die is 35 kg and it falls from a height of 2 m, we need to find the work done to cause a depth of indentation of 10 mm (0.01 m).
The work done (W) is also equal to the change in potential energy (P.E.):
W = P.E.
P.E. = mgh
Where:
m = mass of the die (35 kg)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height from which the die falls (2 m)
Substituting the values into the formula:
P.E. = (35 kg) × (9.8 m/s²) × (2 m)
P.E. = 686 Joules
Since the work done (W) is equal to the change in potential energy (P.E.), we have:
W = 686 Joules
Now, we can find the average stamping force (F) using the formula:
F = W ÷ d
Where:
W = work done (686 Joules)
d = displacement (indentation depth, 0.01 m)
Substituting the values into the formula:
F = (686 Joules) ÷ (0.01 m)
F = 68,600 Newtons
The average stamping force is 68,600 Newtons.