Physics, 28.02.2021 17:40, spyderpunch69

The ratio of the diameters of the small piston to the large piston of a hydraulic lift is 1:10. Find (a) the ratio of the force on the small piston to the force on the large piston and (b) the ratio of the pressure on the small piston to the pressure on the big piston.

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answered: esnyderquintero

a) 1: 100 F₂ = 100 F₁, b) P₁ = P₂ 1:1

Explanation:

The pressure in a system is the same for a given horizontal line, therefore

P₁ = P₂

where subscript 1 is for small piston and index 2 is for large piston 2

a) they ask the relation of the forces

pressure is defined by

P = F / A

for the small piston

P₁ = F₁ / A₁

the area of the piston is

A₁ =π r₁²

P₁ = F₁ /π r₁²

for big piston

P₂ = F₂ / A₂

in the exercise indicates that the diameter of the large piston is 10 times the diameter of the small piston

A = π r₂²

r₂ = 10 r₁

r₂ = π 10² r₁²

we substitute

P₂ = $\frac{F_2}{ \pi \ 100 \ r_1^2}$

we equalize the pressures

$\frac{F_1 }{ \pi \ r_1^2 } = \frac{F_2}{ \pi \ 100 r_1^2}$

F₁ = F₂ / 100

F₂ / F₁ = 100

therefore the force ratio is

1: 100

b) according to Pascal's principle for the same height the pressure is the same regardless of the shape of the container, therefore the pressure of the two pistons is the same

P1 = P2

1: 1

answered: Guest

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

$_a^z\textrm{x}\rightarrow _{a-2}^{z-4}+_2^4\alpha$

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

$_a^z\textrm{x}+_{-1}^0\textrm{e}\rightarrow _{z-1}^a\textrm{y}$

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases $\gamma -radiations$ . this process does not change the mass number.

$_a^z\textrm{x}^*\rightarrow _a^z\textrm{x}+_0^0\gamma$

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as $\beta ^+$ -decay. in this the mass number remains same.