a train cuz its 120km in 3 hours
An electric bulb rated 100 W, 100 V has to be
operated aross 141.4 V, 50 Hz A.C. supply. The
capacitance of the capacitor which has to be
connected in series with bulb so that bulb will
glow with full intensity is [NCERT Pg. 251]
Answer:
The capacitance of the capacitor is 31.84 μF.
Explanation:
Given;
power rating of the bulb, P = 100 W
voltage rating of the bulb, Vr = 100 V
operating voltage of the bulb, V= 141.4 V
frequency of the AC = 50 Hz
P = IV = 100 W
V = 100 V
I =
Ic = 1 A
The voltage across the capacitor is given by;
[tex]V_c = \sqrt{V^2 - V_R^2} \\\\V_c = \sqrt{141.4^2 - 100^2} \\\\V_c =99.97 \ V[/tex]
[tex]V_c = I_cX_c\\\\V_c = I_C* \frac{1}{2\pi fC}\\\\ 99.97 = 1 * \frac{1}{2\pi *50 *C}\\\\ C=\frac{1}{2\pi *50*99.97}\\\\ C = 31.84*10^{-6} \ F\\\\C = 31.84 \ \mu F[/tex]
Therefore, the capacitance of the capacitor is 31.84 μF.
A shopper pushes a cart 40.0 m south down one aisle and then turns 90.0° and moves 15.0 m. He then makes another 90.0° turn and moves 20.0 m. Find the shopper’s total displacement.
Answer:
25.0mExplanation:
Find the diagram attached for the schematic diagram of motion of the cart. The displacement of the cart is the length AD.
To get the length AD, we will apply Pythagoras theorem on ΔAED.
According to the theorem:
AD² = AE²+ED²
AD² = 20²+15²
AD² = 400+225
AD² = 625
AD = √625
AD = 25.0m
Hence the shopper’s total displacement is 25.0m
You release a ball from rest at the top of a ramp. 6 s later it is moving at 4.0
m/s. What is the acceleration? (in meters per second squared) *
Your answer
[tex]a = \frac{vf - vi}{t} [/tex]
here initial velocity vi=0 as ball release from rest
the final velocity is vf=4.0
time is t=6
so putting all these values in above equation
[tex]a = \frac{ 4.0- 0}{6} [/tex]
[tex]a = 0.6667m \s {}^{2} [/tex]
I am a cell. I am long and thin. I reach all the way from the brain
to the tip of a finger. I have a special coat of fat that helps me do
my job. My job is to send electrical signals from one part of the
body to another.
Answer:
Neurons
Explanation:
We humans have a nervous system that coordinates our behavior and transmits signals between different parts of our body.
Now, this nervous system contains a lot of nerve cells which we call Neurons. These Neurons have a cell like body and their job is to transmit signals from one part of our body to another.
Thus, the cell is called Neurons.
A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the plates are pulled apart to twice their original separation. This process will double the: __________A. capacitance
B. surface charge density on each plate
C. stored energy
D. electricfield between the two places
E. charge on each plate"
Answer: C.
Explanation:
For a parallel-plate capacitor where the distance between the plates is d.
The capacitance is:
C = e*A/d
You can see that the distance is in the denominator, then if we double the distance, the capacitance halves.
Now, the stored energy can be written as:
E = (1/2)*Q^2/C
Now you can see that in this case, the capacitance is in the denominator, then we can rewrite this as:
E = (1/2)*Q^2*d/(e*A)
e is a constant, A is the area of the plates, that is also constant, and Q is the charge, that can not change because the capacitor is disconnected.
Then we can define:
K = (1/2)*Q^2/(e*A)
And now we can write the energy as:
E = K*d
Then the energy is proportional to the distance between the plates, this means that if we double the distance, we also double the energy.
If the plates are pulled apart to twice their original separation, then this will double the stored energy. Hence, option (C) is correct.
The given problem is based on the concept of parallel plat capacitor. For a parallel-plate capacitor where the distance between the plates is d.
The capacitance is:
C = e*A/d
here.
e is the permittivity of free space.
Since, the distance is inversely proportional then if we double the distance, the capacitance halves. Now, the stored energy can be given as,
E = (1/2)*Q^2/C
here,
Q is the charge stored in the capacitor.
Now you can see that in this case, the capacitance is in the denominator, then we can rewrite this as:
E = (1/2)*Q^2*d/(e*A)
e is a constant, A is the area of the plates, that is also constant, and Q is the charge, that can not change because the capacitor is disconnected.
Then we can define:
K = (1/2)*Q^2/(e*A)
And now we can write the energy as:
E = K*d
So, the energy is proportional to the distance between the plates.
Thus, we can conclude that if the plates are pulled apart to twice their original separation, then this will double the stored energy. Hence, option (C) is correct.
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How will the motion of an object that is moving to the right change, if it is pushed in the opposite direction with a greater force?
Оооо
The object will move at a constant speed in the same direction for a while and then slow down and stop.
The object will slow down for a while and then move at a slower constant speed in the same direction.
The object will slow down and then begin to move faster and faster in the opposite direction.
0 The object will speed up and then begin to move at a slower speed in the opposite direction.
A student rides a bicycle 2400 meters in four minutes to get to school. What is the student's speed?
Answer:
10 mls2
Explanation:
speed =distance /time
A velocity selector uses a fixed electric field of magnitude E and the magnetic field is varied to select particles of various energies. If the electric field strength is 2.2 x 104 N/C, what should be the value of the magnetic field (in tesla) to select protons of velocity 6.4 x 105 m/s
Answer:
The value is [tex]B = 0.034 \ T [/tex]
Explanation:
From the question we are told that
The electric field strength is [tex]E = 2.2*10^{4} \ N/C[/tex]
The velocity is [tex]v = 6.4 *10^{5} \ m/s[/tex]
Generally the magnetic field is mathematically represented as
[tex]B = \frac{E}{v}[/tex]
=> [tex]B = \frac{2.2*10^{4}}{6.4 *10^{5}}[/tex]
=> [tex]B = 0.034 \ T [/tex]
Jumping on a trampoline cause you to fly up in the air. What type of newton’s law is it ?
Answer:
The Third law
Explanation:
For every action there is an equal and opposite reaction.
Answer:
First Law
Explanation:
An object at rest (not moving) will stay at rest unless an unbalanced force acts on it.
An object in motion will stay in motion (in a straight line and at a constant speed) unless an unbalanced force acts on it.
You jump down on a trampoline and fly up in the air as a result.
During a thunderstorm the electric field at a certain point in the earth's atmosphere is 1.07 105 N/C, directed upward. Find the acceleration of a small piece of ice of mass 1.08 10-4 g, carrying a charge of 1.05 10-11 C.
Answer:
The acceleration of a small piece of ice is 10.40 m/s².
Explanation:
The electric force is given by:
[tex]F = Eq[/tex]
Where:
E is the electric field = 1.07x10⁵ N/C
q is the charge = 1.05x10⁻¹¹ C
The electric force is equal to Newton's second law:
[tex] Eq = ma [/tex]
Where:
m is the mass = 1.08x10⁻⁴ g = 1.08x10⁻⁷ kg
a is the acceleration
Hence, the acceleration is:
[tex] a = \frac{Eq}{m} = \frac{1.07 \cdot 10^{5} N/C*1.05 \cdot 10^{-11} C}{1.08 \cdot 10^{-7} kg} = 10.40 m/s^{2} [/tex]
Therefore, the acceleration of a small piece of ice is 10.40 m/s².
I hope it helps you!
Explain how Dirty Deeds Done Dirt Cheap works. (JoJo's bizarre adventure) for an essay
Answer:
dirty deeds done dirt cheap goes to different dimensions with american flag,and usually grabs alternate versions of his user
Explanation:
Answer:
Daga Kotowaru
Explanation:
One of my favourite things to say is to say No to people who desparately need help
help me get the answer in Physical Science.
Answer:
lithium
Explanation:
I took physical science 2 years ago and passed with an A
A student must design an experiment to determine the relationship between the mass of an object and the resulting acceleration when the object is under the influence of a net force. Which of the following experiments should the student conduct in order to determine the relationship between all three quantities?
Answer choices:
A) Drop objects of different masses from a known height above the ground for multiple trials such that they reach their respective terminal speeds. Use a stopwatch to measure the time it takes each object to reach the ground, and record the mass of each object by using a mass scale.
B) Slide objects of different masses across the same rough surface so that each object travels at a constant speed while under the influence of the force of kinetic friction. Then measure the force required to keep each object at a constant speed by using a force sensor, and record the mass of each object by using a mass scale. Perform this experiment multiple times with objects of different masses.
C) Place an object on a rough surface so that the object is at rest. Use a force sensor to exert a force on the object until just after the object overcomes the force of static friction. Record this force. Repeat the experiment for objects of different masses.
D) Slide an object of known mass across a rough surface, using a constant applied force that can be measured by a force sensor. Place a motion detector behind the object so that its speed can be measured as it slides across the surface. Repeat the experiment for different applied forces.
Answer:
D) Slide an object of known mass across a rough surface, using a constant applied force that can be measured by a force sensor. Place a motion detector behind the object so that its speed can be measured as it slides across the surface. Repeat the experiment for different applied forces.
Explanation:
"The motion detector will provide information about the object’s speed as a function of time as it slides as a result of the applied force. The information about the object’s speed as a function of time can be used to determine the acceleration of the object. The force sensor measures the applied force exerted on the object, and the mass of the object is known. Therefore, this experiment can be used to determine how an object’s mass is related to the net force exerted on the object and the acceleration of the object."
It cannot be A because we need an acceleration will be determined by gravity.
It cannot be B because the term constant speed means that there is no net force, which is required by the initial question.
It cannot be C because the experiment is good for determining the coefficient of friction but not for determining how the mass relates to the acceleration.
It must be D because the object is moving and we have a motion detector, we can graph the acceleration vs time graph. So D allows you to have a lot of the different acceleration values which helps with determining the relationship between acceleration and the mass.
a jogger travels at 4 m/s for 100 s what is the distance covered
400m
Explanation:
given,
v= 4m/s
t= 100s
d= ?
since, v = d / t
therefore, d = v * t (velocity multiplied by time)
=> d = 4 * 100
= 400m.
plzzz help its for my civics class what answer is it????????????
Answer:
the correct answer is The English Bill of Rights
Explanation:
This is the answer because i have taken the test.
4. A teacher throws the stapler at her students 23 m in 1.2 seconds. What speed must the teacher throw the
stapler and what will be the staplers highest point during its flight?
dy = - 42gt2
dx = Vyt
Answer:
dy
Explanation:
My guess of guts.
okay bye
The emf of the battery is 1.5 V. In Nichrome there are 9 × 1028 mobile electrons per m3, and the mobility of mobile electrons is 7 × 10−5 (m/s)/(N/C). Each thick wire has length 29 cm = 0.29 m and cross-sectional area 9 × 10−8 m2. The thin wire has length 6 cm = 0.06 m and cross-sectional area 1.3 × 10−8 m2. (The total length of the three wires is 64 cm.) In the steady state, calculate the number of electrons entering the thin wire every second. Do not make any approximations, and do not use Ohm's law or series-resistance equations.
Answer:
The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
Explanation:
Given;
emf of the battery, V = 1.5 V
electron density, = 9 × 10²⁸ mobile electrons per m³
mobility of electron, u = 7 × 10⁻⁵ (m/s)/(N/C)
length of thin wire, L = 6 cm = 0.06 m
cross sectional area of the thin wire, A = 1.3 x 10⁻⁸ m²
The magnitude of the electric field in the thin wire is given by;
E = V/L
E = (1.5) / (0.06)
E = 25 N/C
the number of electrons entering the thin wire every second is given by;
[tex]e/s = mobility \ x \ Electric \ field\\\\number \ of \ electrons \ per \ second =\frac{7*10^{-5} (m/s)}{N/C} *25 (N/C)\\\\number \ of \ electrons \ per \ second = 1.75*10^{-3} \ m/s[/tex]
Therefore, the number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
Calculation of the number of electrons:Since
emf of the battery, V = 1.5 V
electron density, = 9 × 10²⁸ mobile electrons per m³
mobility of electron, u = 7 × 10⁻⁵ (m/s)/(N/C)
length of thin wire, L = 6 cm = 0.06 m
cross sectional area of the thin wire, A = 1.3 x 10⁻⁸ m²
So here the magnitude should be
E = V/L
E = (1.5) / (0.06)
E = 25 N/C
Now the number of electrons should be
= 7 × 10⁻⁵ *25
= 1.75 x 10⁻³ mobile
hence, The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
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g A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 1.97 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 1680 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 4.34 V/m, (b) in the negative z direction and has a magnitude of 4.34 V/m, and (c) in the positive x direction and has a magnitude of 4.34 V/m
Answer:
a) 1.22*10^-18 N in the positive z direction
b) 1.65*10^-19 N in the negative z direction
c) (6.94*10^-19 N) in the positive x direction + (5.30*10^-19 N) in the positive z direction
Explanation:
See attachment for calculations
(a) The electromagnetic force on the proton is 1.224 × 10⁻¹⁸ [tex]\hat k[/tex] N
(b) The force is 1.65 × 10⁻¹⁹ [tex](-\hat k)[/tex] N
(c) The force is (6.94 [tex]\hat i[/tex] + 5.29 [tex]\hat k[/tex]) × 10⁻¹⁹ N
Electromagnetic force on the proton:Given a proton moving in the positive y-direction with a speed of :
v = 1680 m/s [tex]\hat j[/tex]
The magnetic field is in the negative x-direction with magnitude:
B = 1.97 mT [tex](-\hat i)[/tex]
(a) Electric field applied in positive z-direction :
E = 4.34 V/m [tex]\hat k[/tex]
The net force on the proton is iven by:
F = q (E + v×B)
where q is the charge on proton, given by:
q = 1.6×10⁻¹⁹ C
So,
F = 1.6×10⁻¹⁹( 4.34 [tex]\hat k[/tex] + 1680 [tex]\hat j[/tex] × 1.97×10⁻³ [tex](-\hat i)[/tex] )
F = 1.6×10⁻¹⁹ ( 4.34 [tex]\hat k[/tex] + 3.309 [tex]\hat k[/tex])
F = 1.224 × 10⁻¹⁸ [tex]\hat k[/tex] N
(b) Electric field applied in negative z-direction :
E = 4.34 V/m [tex](-\hat k)[/tex]
The net force on the proton is iven by:
F = q (E + v×B)
where q is the charge on proton, given by:
q = 1.6×10⁻¹⁹ C
So,
F = 1.6×10⁻¹⁹( 4.34 [tex](-\hat k)[/tex] + 1680 [tex]\hat j[/tex] × 1.97×10⁻³ [tex](-\hat i)[/tex] )
F = 1.6×10⁻¹⁹ ( 4.34 [tex](-\hat k)[/tex] + 3.309 [tex]\hat k[/tex])
F = 1.65 × 10⁻¹⁹ [tex](-\hat k)[/tex] N
(c) Electric field applied in positive x-direction :
E = 4.34 V/m [tex]\hat i[/tex]
The net force on the proton is iven by:
F = q (E + v×B)
where q is the charge on proton, given by:
q = 1.6×10⁻¹⁹ C
So,
F = 1.6×10⁻¹⁹( 4.34 [tex]\hat i[/tex] + 1680 [tex]\hat j[/tex] × 1.97×10⁻³ [tex](-\hat i)[/tex] )
F = 1.6×10⁻¹⁹ ( 4.34 [tex]\hat i[/tex] + 3.309 [tex]\hat k[/tex])
F = (6.94 [tex]\hat i[/tex] + 5.29 [tex]\hat k[/tex]) × 10⁻¹⁹ N
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A particle moves along a path described by y=Ax^3 and x = Bt, where tt is time. What are the units of A and B?
Answer:
In a nutshell, units of A and B are [tex]\frac{1}{[l]^{2}}[/tex] and [tex]\frac{[l]}{[t]}[/tex], respectively.
Explanation:
From Dimensional Analysis we understand that [tex]x[/tex] and [tex]y[/tex] have length units ([tex][l][/tex]) and [tex]t[/tex] have time units ([tex][t][/tex]). Then, we get that:
[tex][l] = A\cdot [l]^{3}[/tex] (Eq. 1)
[tex][l] = B\cdot [t][/tex] (Eq. 2)
Now we finally clear each constant:
[tex]A = \frac{[l]}{[l]^{3}}[/tex]
[tex]A = \frac{1}{[l]^{2}}[/tex]
[tex]B = \frac{[l]}{[t]}[/tex]
In a nutshell, units of A and B are [tex]\frac{1}{[l]^{2}}[/tex] and [tex]\frac{[l]}{[t]}[/tex], respectively.
A daring stunt woman sitting on a tree limb
wishes to drop vertically onto a horse gallop-
ing under the tree. The constant speed of the
horse is 6.8 m/s, and the woman is initially
1.91 m above the level of the saddle.
How long is she in the air? The acceleration
of gravity is 9.8 m/s.
Answer in units of s.
Answer:
she is in the air for approximately 0.62 seconds
Explanation:
We want to find the time for a free fall under the acceleration of gravity, covering a distance of 1.91 m, and considering that the woman doesn't impart initial velocity in the vertical direction. So we use the kinematic equation:
[tex]d=v_i\,t+ \frac{g}{2} \,t^21.91 = 0 +4.9\, t^2\\t^2=1.91/4.9\\t=\sqrt{1.91/4.9} \\t\approx 0.624\,\,sec[/tex]
Then she is in the air for approximately 0.62 seconds
You have a friend who reports that he falls asleep easily around 11 PM but then awakens for about an hour most nights around two or 3 AM he seems near exhausted what would be the traditional exclamation for his problem how much the information contribute by anthropologists change this view? Give the anthropological view what recommendations would you make your friend?
It is highly recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.
What is insomnia?Insomnia is a medical condition in which an individual is unable to sleep or has short periods of interrupted sleep.
A friend who falls asleep easily and then has difficulty going to sleep is probably suffering from insomnia.
It is recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.
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A steel ball moves from a position of +125 meters to a position of -75 meters. This motion takes 90.0 seconds. What is the velocity of the steel ball?
Answer:
2.22m/s to the left
Explanation:
Given parameters:
Initial position = +125m
Final position = -75m
Motion time = 90s
Unknown:
Velocity of the steel ball = ?
Solution:
The velocity of the steel ball is given as the displacement divided by the time;
Velocity = [tex]\frac{displacement}{time}[/tex]
The net displacement of the ball = 125- (-75) = 200m to the left
Input the parameters and solve for the velocity;
Velocity = [tex]\frac{200}{90}[/tex] = 2.22m/s to the left
The public is not yet able to purchase cars powered by hydrogen fuel cells because engineers have to determin
how the cars perform based on which scenario?
on racetracks
Answer:
The options are
A.on racetracks
B.in real-world conditions
C.in flooded environments
D.on closed courses
The answer is B. In real world conditions
The public is not yet able to purchase cars powered by hydrogen fuel cells because engineers have to determin
how the cars perform based on real world conditions.
This will ensure they encounter the real and first hand experiences about the challenges and also the advantages associated with using this type of fuel.
If a car is traveling at an average speed of 70 kilometers per hour how long does it take the car to travel 14 kilometers
Answer:
Explanation:
O.20 hour A
If a car is traveling at an average speed of 70 kilometers per hour, 0.2 hours it takes the car to travel 14 kilometers.
What is average speed?By multiplying the distance that an item travels in one unit by the amount of time it takes to go that distance, one may determine the speed of the object. The speed of the item on this voyage, denoted by the letter "s," is equal to s = D/T if "D" is indeed the distance traveled in certain time "T."
Understanding average speed will help you better comprehend the pace of a travel. On a travel, the pace could occasionally change. Knowing the average speed then becomes crucial to getting an idea of how quickly the route will be finished.
Distance covered = average speed × Time travelled
14=70× Time travelled
Time travelled = 0.2 hours
Therefore, 0.2 hours it takes the car to travel 14 kilometers.
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While you were at the skate park, what did you notice about potential and kinetic energy
Answer: I only know that the skater riding down the ramp increeses it's kinetic energy.
Explanation:
the diagram shows a contour map. letter a through k are reference points on the map. which points are located at the same elevation above sea level?
Answer:
K and I
Explanation:
Contour maps use lines that represent spaces in a map that have the same elevation, this means that all the lines should be continuous and closed, in this case, we are not able to see the full extent of most of the lines, but since the points are located in different lines we can assume that they are at different heights, so since only point K and point I are on the same line, we know that these two points are at the same height.
PLEASE HELP
A sharpshooter fires a 0.22 caliber rifle horizontally at 100 m/s at a target 75m away. How far does the
bullet drop by the time it reaches the target?
This question involves the concept of semi-projectile motion. It can be solved using the equations of motion in the horizontal and the vertical motion.
The bullet drops "2.76 m" by the time it reaches the target.
First, we will analyze the horizontal motion. We assume no air resistance, so the horizontal motion will be uniform. Hence, using the equation of uniform motion here to find the total time to reach the target:
[tex]s = vt\\\\t = \frac{s}{v}[/tex]
where,
s = distance = 75 m
v = velocity = 100 m/s
t = time = ?
Therefore,
[tex]t = \frac{75\ m}{100\ m/s}[/tex]
t = 0.75 s
Now, we will analyze the vertical motion of the bullet. We will use the second equation of motion in the vertical direction to find the height dropped by the bullet.
[tex]h = v_it+\frac{1}{2}gt^2[/tex]
where,
h = height dropped = ?
vi = initial vertical speed = 0 m/s
t = time interval = 0.75 s
g = acceleration due to gravity = 9.81 m/s²
therefore,
[tex]h = (0\ m/s)(0.75\ s)+\frac{1}{2}(9.81\ m/s^2)(0.75\ s)^2[/tex]
h = 2.76 m
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The attached picture shows the equations of motion in the horizontal and vertical directions.
To begin your activity, open this Tracker experiment: Car Round Trip. Click play to watch the video. The other video controls allow you to rewind the video or step forward or backward one frame at a time.
Answer:
The car appears to have a constant, positive acceleration for most of the video clip.
500m=?m² va rooooooog
Answer:
250000 [m²]
Explanation:
A unit analysis has to be performed, where the unit of length is the meter. And the unit for the area is the square meter (m²)
L = 500 [m]
Therefore if we want to convert this length to meters we must square the length.
A = 500² = 500*500 = 250000 [m²]
g A hydraulic press has a safety feature which consists of a hydraulic cylinder with a piston at one end and a safety valve at the other. The cylinder has a radius of 0.0200 m and the safety valve is simply a 0.00750-m radius circular opening at one end, sealed with a disk. The disk is held in place by a spring with a spring constant of 950 N/m that has been compressed 0.0085 m from its natural length. Determine the magnitude of the minimum force that must be exerted on the piston in order to open the safety valve.
Answer:
58.32 N
Explanation:
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
where r is the radius of the circle.
The cylinder has a radius of 0.02 m, its area is;
[tex]A_{1}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.02)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 0.0004
= 1.2571 x [tex]10^{-3}[/tex]
Area of the cylinder is 0.0013 [tex]m^{2}[/tex].
The safety valve has a radius of 0.0075 m, its area is;
[tex]A_{2}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.0075)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 5.625 x [tex]10^{-5}[/tex]
= 1.7679 x [tex]10^{-4}[/tex]
Area of the valve is 0.00018 [tex]m^{2}[/tex].
From Hooke's law, the force on the safety valve can be determined by;
F = ke
[tex]F_{2}[/tex] = 950 x 0.0085
= 8.075 N
Minimum force, [tex]F_{1}[/tex], required can be determined by;
[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]
[tex]\frac{F_{1} }{0.0013}[/tex] = [tex]\frac{8.075}{0.00018}[/tex]
[tex]F_{1}[/tex] = [tex]\frac{0.0013 *8.075}{0.00018}[/tex]
= 58.32
The minimum force that must be exerted on the piston is 58.32 N.