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2 years ago

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A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 16.0 cm. What force must be applied to the

smaller piston to obtain a force of 3200 N at the larger piston?

1 answer:

SVETLANKA909090 [29]2 years ago

5 0

Answer:

<em>The force applied to the smaller piston = 2512 N</em>

Explanation:

Hydraulic press: A hydraulic press is a device used to produce a very large force. A hydraulic force operates based on pascal's principle.

F/f = A/a................ Equation 1

making f the subject of the equation above

f =(F×a)/A............. Equation 2

Where F = Force on the larger piston, f = force on the smaller piston, A = area of the larger piston, a = area of the smaller piston.

<em>Given: F = 3200 N, and</em>

<em>Area (A) = πD²/4 where D = 16.0 cm = 0.16 m</em>

<em>A = 3.143×(0.16)²/4 = 0.02 m²</em>

<em>Also</em>

<em>a = πd²/4 where d = 2 cm = 0.02 cm</em>

<em>a = 3.143×(0.02)²/4</em>

<em>a = 0.0157 m²</em>

<em>Substituting these values into equation 2</em>

<em>f = (3200×0.0157)/0.02</em>

<em>f = 2512 N</em>

<em>The force applied to the smaller piston = 2512 N</em>

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The magnitude of the average force that the ball exerts against his glove is 600 N

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<h3>Further explanation</h3>

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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<u>Given:</u>

mass of ball = m = 0.15 kg

initial speed of ball = u = 40 m/s

final speed of ball = v = 0 m/s

distance = d = 20 cm = 0.2 m

<u>Asked:</u>

average force = F = ?

<u>Solution:</u>

<em>We will use </em><em>Newton's Law of Motion</em><em> to solve this problem as follows:</em>

$F = m a$

$F = m (\frac { u^2 - v^2 } { 2d } )$

$F = 0.15 \times \frac { 40^2 - 0^2 } { 2 \times 0.2 }$

$F = 0.15 \times \frac { 1600 } { 0.4 }$

$F = 0.15 \times 4000$

$\boxed {F = 600 \texttt{ N}}$

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<h3>Learn more</h3>

Impacts of Gravity : brainly.com/question/5330244
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<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Dynamics

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