Question

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height . The mass of each object is a multiple of the base mass : object 1 has mass 3.10 , object 2 has mass 1.46 , and object 3 has mass . When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23 ,

Answer 1

The definition of gravitational potential energy would gravitate allows to find the answers for the energy of each object on the highest rung of the ladder are:

 a) expression for gravitational potential energy is  $U_p = m g \ \Delta y$

 b) Energy value

        * Body 1    U_p = 82 J

        * Body 2   U_p = 38.6 J

        * Body  3  18.5 J

The gravitational potential energy is a configuration energy that represents the amount of work that the system can do for a given configuration, its expression is

           $U_p = m g \ \Delta y$

Where $U_p$ is the gravitational potential energy, m the mass of the body and Δy the difference in height.

In this case it indicates that the minimum height is at the bottom and is equal to zero, the steps of a ladder have a height of approximately y = 15 cm = 0.15 m

They indicate the mass of the bodies are m₁ = 3.10 kg, the mass of the body 2 m₂ = 1.46 kg , the mass of the third object is not observed, suppose it is m₃ = 0.7 kg.

They indicate that the body is placed on the last step, suppose it is a standard 18-step ladder, therefore the total height is

          y = # _ steps    y_each step

          y = 18   0.15

          y = 2.70 m

the gravitational potential energy to the capacity of the body is

body 1

              $U_p$ = m₁ g Δy₁

              U_p = 3.10  9.8 (2.70 -0)

               U_p = 82 J

body 2

              U_p = 1.46 9.8 ( 2.7-0)

              U_p = 38.6 J

body  3

             U_pUp = 0.70 9.8 (2.7-0)

             U_p = 18.5 J

In conclusion, using the definition of gravitational potential energy, we can find the answers for the energy of each object on the highest rung of the ladder are;

     a) expression for gravitational potential energy is  $U_p = m g \ \Delta y$

     b) Energy value

        * Body 1    U_p = 82.0 J

        * Body 2   U_p = 38.6 J

        * Body  3   U_p = 18.5 J

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