A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.7 J of work to compress the spring by 0.20 m . If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s2 . Find the value of

(a) the spring constant and
(b) the mass.

(a) 185 N/m

(b) 3.083 kg

Explanation:

(a)

Using,

E = 1/2ke² Equation 1

Where E = work done to compress the spring, k = spring constant of the spring, e = compression of the spring.

make k the subject of the equation

k = 2E/e² Equation 2

Given: E = 3.7 J, e = 0.20 m

Substitute into equation 2

k = 2(3.7)/0.2²

k = 185 N/m.

(b)

Using,

F = ma Equation 2

Where F = force applied to the spring, m = mass attached to the spring, a = acceleration of the spring.

But from hook's law,

F = ke Equation 3

substitute equation 3 into equation 2

ke = ma

make m the subject of the equation

m = ke/a Equation 4

Given: k = 185 N/m, e = 0.2 m, a = 12 m/s²

Substitute into equation 4

m = 185(0.2)/12

m = 3.083 kg

(a) the spring constant is 185 N/m

(b) the mass is 3.083 kg

Explanation:

Given;

work done in compressing the spring, W = 3.7 J

extension of the spring, x = 0.20 m

acceleration of the spring, a =  12 m/s²

Part (a) the spring constant

W = ¹/₂kx²

where;

w is work done

k is the spring constant

x is the extension of the spring

k = 2W / x²

k = ( 2 x 3.7) / (0.2²)

k = 185 N/m

Part (b) the mass

From Newton's second law of motion;

F = ma

Also from Hook's law;

F = kx

Equate the two laws;

ma = kx

m = kx / a

m = (185 x 0.2) / (12)

m = 3.083 kg

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this

explanation:

considering the bohr theory, the type of connection that requires the transfer the answer conuldn't be right