Map The answer to each of the following questions can be written as a numeric co

Question

Map The answer to each of the following questions can be written as a numeric coefficient times some combination of the variables m, g, and d (representing mass, acceleration due to gravity, and the height of one step, respectively). The appropriate combination of variables is indicated. Enter only the numeric coefficient (Example: If the answer is 1.23mgd, just enter 1.23) Three different objects, all with different masses, are initially resting at the bottom of a set of steps, each with a uniform height d. In this position, the total gravitational potential energy of the three obiect system is said to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? 4.60m Number mgd g,system 2.21 m This potential energy was calculated relative to the bottom of the stairs. If you were to redefine the reference height such that the total potential energy of the system becomes zero, how high above the bottom of the stairs would the new reference height be? Number original reference height Now, find a new reference height (measured again from the bottom of the stairs) such that the highest two objects have the exact same potential energy Number

Explanation / Answer

Ug system = (m1*g*d) +(m2*g*2d) + (m3*g*3d)

Ug = (m*g*d)+(2.21*m*2d)+(4.6*m*g*3d)

Ug = 19.22 mgd

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(m1+m2+m3)*g*h = Ug

h = 19.22*m*g*d/(m + 2.21m + 4.6m)g

h = 2.46d

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m2 = 2.21 m

m3 = 4.6 m

m2 < m3

height of m2 , h2 > h3

u2 = u3

m2*g*(h3+d) = m3*g*h3

2.21*m*g*(h3+d) = 4.6*m*g*h3

2.21h3 + 2.21d = 4.6 h3

h3*(4.6-2.21) = 2.21d

h3 = 0.925 d

the mass 4.6m is at height of 0.925 d from the bottom

and the mass 2.21 is at a height of 1.925 d

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