A force of 250 N is applied to a hydraulic jack piston that is 0.01 m in diameter. If the piston which supports the load hasa diameter of 0.10 m, approximately how much mass can belifted. Ignore any difference in height between the pistons.

postillan4

postillan4

Answered question

2021-02-21

A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01 meters in diameter. If the piston which supports the load hasa diameter of 0.10 m, approximately how much mass can belifted. Ignore any difference in height between the pistons.

Answer & Explanation

Szeteib

Szeteib

Skilled2021-02-22Added 102 answers

P1=P2 
F1A1=F2A2 
F1πr12=F2πr22 
you can revoke the "π"s on both sides then you solve for F
and you have: 
F2=F1(r2r1)2 
remember diameter = 2 * radius... the force you obtain (f2) represents the maximum weight that can be lift

xleb123

xleb123

Skilled2023-06-19Added 181 answers

The pressure exerted by the force on the small piston can be calculated using the formula:
P1=FA1
where P1 is the pressure, F is the force, and A1 is the area of the small piston.
The pressure is transmitted to the large piston, so we can set it equal to the pressure on the large piston:
P1=P2
Using the formula for pressure on the large piston:
P2=FliftedA2
where Flifted is the force that can be lifted and A2 is the area of the large piston.
Equating the two pressures:
FA1=FliftedA2
Solving for Flifted:
Flifted=F·A2A1
Given that the force F is 250 Newtons, the diameter of the small piston is 0.01 meters, and the diameter of the large piston is 0.10 meters, we can calculate the areas as follows:
A1=π4·(0.01)2
A2=π4·(0.10)2
Substituting these values into the equation for Flifted:
Flifted=250·π4·(0.10)2π4·(0.01)2
Simplifying:
Flifted=250·0.1020.012
Calculating:
Flifted25000 Newtons
Therefore, approximately 25,000 Newtons of mass can be lifted.
Jazz Frenia

Jazz Frenia

Skilled2023-06-19Added 106 answers

Step 1:
The formula to calculate pressure is given by:
P=FA
where:
P is the pressure,
F is the force applied, and
A is the area on which the force is applied.
Given that the force applied is 250 Newtons and the diameter of the smaller piston is 0.01 meters, we can calculate the area (A1) using the formula for the area of a circle:
A1=π·d124 where d1 is the diameter of the smaller piston.
Substituting the values, we have:
A1=π·(0.01m)24
Step 2:
Next, let's calculate the pressure (P1) applied to the smaller piston:
P1=FA1
Substituting the given force and calculated area, we get:
P1=250Nπ·(0.01m)24
Now, according to Pascal's law, this pressure is transmitted equally to the larger piston. The pressure (P2) acting on the larger piston is the same as P1:
P2=P1
Step 3:
Next, we can calculate the force (F2) acting on the larger piston using the formula for pressure:
P2=F2A2 where A2 is the area of the larger piston. We can calculate A2 using the same formula as before:
A2=π·d224 where d2 is the diameter of the larger piston.
Substituting the given diameter, we get:
A2=π·(0.10m)24
Now, let's solve for F2:
P2=F2A2
Substituting P2 (which is equal to P1) and A2, we have:
P1=F2π·(0.10m)24
Step 4:
Finally, we can rearrange the equation to solve for F2:
F2=P1·π·(0.10m)24
Now we have the force acting on the larger piston. To determine the mass that can be lifted, we can use Newton's second law:
F=m·g
where:
F is the force applied (in this case, F2),
m is the mass, and
g is the acceleration due to gravity.
Rearranging the equation to solve for m:
m=Fg
Substituting the value of F2 and taking g as approximately 9.8 m/s², we can calculate the mass:
m=F29.8m/s2
Substituting the value of F2 calculated earlier, we get:
m=P1·π·(0.10m)249.8m/s2
Simplifying this expression will give us the approximate mass that can be lifted.
fudzisako

fudzisako

Skilled2023-06-19Added 105 answers

Result: 0.255 kg
Solution:
Flarger=Fsmaller·AsmallerAlarger
where:
Flarger is the force exerted by the larger piston,
Fsmaller is the applied force on the smaller piston,
Asmaller is the area of the smaller piston, and
Alarger is the area of the larger piston.
Given that the force applied on the smaller piston is 250N, the diameter of the smaller piston is 0.01m, and the diameter of the larger piston is 0.10m, we can calculate the mass that can be lifted.
First, let's calculate the areas of the pistons:
Asmaller=π·dsmaller24=π·(0.01m)24
Alarger=π·dlarger24=π·(0.10m)24
Substituting the given values, we can calculate the areas:
Asmaller=π·0.00014m2
Alarger=π·0.014m2
Now, we can substitute the values of the forces and areas into the formula to calculate the force exerted by the larger piston:
Flarger=250N·π·0.00014π·0.014
Simplifying the expression, we get:
Flarger=250·0.00010.01N
Calculating further:
Flarger=2.5N
Finally, to calculate the mass that can be lifted, we can use the formula:
Force=mass·acceleration
Since the acceleration due to gravity is 9.8m/s2, we can rearrange the formula to solve for mass:
mass=Forceacceleration
Substituting the values, we have:
mass=2.5N9.8m/s2
Calculating the mass, we find:
mass0.255kg
Therefore, approximately 0.255 kg of mass can be lifted.

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