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3 years ago

Can you please explain hooks law?

Physics

2 answers:

True [87]3 years ago

8 0

Explanation:

Hooke's law is a law of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance—that is, Fₛ = kx, where k is a constant factor characteristic of the spring, and x is small compared to the total possible deformation of the spring.

Naily [24]3 years ago

6 0

Hooke's Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance is proportional to that distance. The law is named after 17th century British physicist Robert Hooke, who sought to demonstrate the relationship between the forces applied to a spring and its elasticity. He first stated the law in 1660 as a Latin anagram, and then published the solution in 1678 as ut tensio, sic vis – which translated, means "as the extension, so the force" or "the extension is proportional to the force").

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A certain planet has a radius of 4990 km. If, on the surface of that planet, a 95.0 kg object has a weight of 591 N, then what i

aniked [119]

Answer:

3743.489 kg

Explanation:

F_g = 591 N

G = 6.674x10^-11 constant of gravity

m_1 = 95 kg

m_2 = unknown

r = 4990*1000 =

F_g = G[(m_1*m_2)/r^2]

591 N = 6.674x10^-11[(95*m_2)/4990^2]

8.855 = [(95*m_2)/4990^2]

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3 years ago

Write the differential equation that governs the motion of the damped mass-spring system, and find the solution that satisfies t

melisa1 [442]

This question is incomplete, the complete question is;

Write the differential equation that governs the motion of the damped mass-spring system, and find the solution that satisfies the initial conditions specified. Units are mks; γ is the damping coefficient, with units of kg/sec

m = 0.2, γ = 1.6 and k = 4

Initial displacement is 1 and initial velocity is -2

x" + _____ x' ____x = 0

x(t) =

Answer:

the solution that satisfies the initial conditions specified is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

Explanation:

Given the data in the question ;

m = 0.2, γ = 1.6, k = 4

x(0) = 1, x'(0) = -2

Now, the differential equation that governs the motions of spring mass system is;

mx" + γx' + kx = 0

so we substitute

0.2x" + 1.6x' + 4x = 0

divide through by 0.2

x" + 8x' + 20x = 0

hence, characteristics equation will be;

m² + 8m + 20 = 0

we find m using; x = [ -b±√(b² - 4ac) ] / 2a

m = [ -8 ± √((8)² - 4(1 × 20 )) ] / 2(1)

m = [ -8 ± √( 64 - 80 ) ] / 2

m = [ -8 ± √-16 ) ] / 2

m = ( -8 ± 4i ) / 2

m = -4 ± 2i

Hence, the general solution of the differential equation is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

From the initial conditions;

c₁ = 1, c₂ = 1

the solution that satisfies the initial conditions specified is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

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Answer:

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