- #1
Resultant force on the piston at the end of stroke
- Thread starter kelvin macks
- Start date
AI Thread Summary
The discussion centers on a homework problem regarding the resultant force on a piston at the end of its stroke, where the expected answer is 4260N, but the poster's calculation yields double that value. The error is attributed to using an incorrect crank radius of 0.12 m instead of the correct 0.06 m, impacting the calculations for tangential velocity and centripetal acceleration. The correct approach involves calculating the tangential velocity and centripetal acceleration using the proper radius, leading to a decelerating force of approximately 4263.67 N. Additionally, there is a reminder that complete solutions are not permitted in the forum.
![IMG_20140616_083027[1].jpg](/data/attachments/54/54326-ad929cd2ee10d39989521d3c9b47e991.jpg?hash=rZKc0u4Q05)
- #2
sankalpmittal
- 785
- 27
kelvin macks said:
The net force acting in an SHM is F=-kx...
You can find k by using the formula of frequency of an SHM.
- #3
dean barry
- 311
- 23
You've maybe put 0.12 m as the crank radius when it should be 0.06 m
r = crank radius = 0.06 metres
w = crank rotation rate = 376.99112 rad / sec
Find the tangential velocity (v) from :
v = w * r
v = 376.99112 * 0.06
v = 22.619 m/s (ANSWER b)
Find the centripetal acceleration (a) :
a = v ² / r
a = 8,527.338 (m/s)/s
The decelerating force (f) = m * a
f = 0.5 * 8,527.338 N
f = 4,263.67 N (ANSWER a)
r = crank radius = 0.06 metres
w = crank rotation rate = 376.99112 rad / sec
Find the tangential velocity (v) from :
v = w * r
v = 376.99112 * 0.06
v = 22.619 m/s (ANSWER b)
Find the centripetal acceleration (a) :
a = v ² / r
a = 8,527.338 (m/s)/s
The decelerating force (f) = m * a
f = 0.5 * 8,527.338 N
f = 4,263.67 N (ANSWER a)
- #4
sankalpmittal
- 785
- 27
dean barry said:
Dude, complete solutions aren't allowed here...
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system
$$M(t) = M_{C} + m(t)$$
$$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$
$$P_i = Mv + u \, dm$$
$$P_f = (M + dm)(v + dv)$$
$$\Delta P = M \, dv + (v - u) \, dm$$
$$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$
$$F = u \frac{dm}{dt} = \rho A u^2$$
from conservation of momentum , the cannon recoils with the same force which it applies.
$$\quad \frac{dm}{dt}...
I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are;
Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction.
Must be LESS than 1 kg.
NO parachutes.
NO glue or Tape can touch the egg.
MUST be able to take egg out in less than 1 minute.
Grade A large eggs will be used.
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