Baggage on the floor of the baggage car of a high-speed train is not prevented from moving other than by friction. The train is travelling down a 5 percent grade when it decreases its speed at a constant rate from 144 mi/h to 66 mi/h in a time interval of 12 s. Determine the smallest allowable value of the coefficient of static friction between a trunk and the floor of the baggage car if the trunk is not to slide.

 μ = 0.36

Explanation:

This exercise must be solved in parts

Let's start by finding the acceleration of the train, using the kinematics relations

         v = v₀ - a t

         a =

let's reduce the magnitudes to the SI system

         v = 66 mi / h (5280 ft / 1mile) (1h / 3600s) = 96.8 ft / s

         v₀ = 144 mi / h = 211.2 ft / s

let's calculate

          a =

          a = - 9.53 ft / s²

Now we can use Newton's second law, for this let's set a reference system with the x axis parallel to the slope of the hill

let's break down the weight

            sin 5 = Wₓ / W

            cos 5 = W_y / W

            Wₓ = W sin 5

            W_y = W cos 5

Y axis

     N- W_y = 0

     N = W cos 5

X axis

      Wₓ -fr = m a

       mg sin 5 - fr = ma

the friction force has the expression

       fr = μ N

       fr = μ W cos 5

we substitute

        mg sin 5 - μ mg cos 5 = ma

        g sin 5 - μ g cos 5 = a

        μ =

        μ =  

let's calculate

       μ = tan 5 - (-9.53) / 32 cos 5

       μ = 0.08749 + 0.2733

       μ = 0.36

-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