Having difficulty finding the PE and KE for these values no mass is given. Does anyone know to go solve these?

11)

12)

13) 50.0 m/s

14) 41.6 m/s

Explanation:

11)

The potential energy of an object is the energy possessed by the object due to its position relative to the ground. It is given by

where

m is the mass of the object

g is the acceleration due to gravity

h is the height relative to the ground

Here in this problem, when the train is at the top, we have:

m = 8325 kg (mass of the train + riders)

(acceleration due to gravity)

h = 127 m (height of the train at the top)

Substituting,

12)

According to the law of conservation of energy, the total mechanical energy of the train must be conserved (in absence of friction). So we can write:

where

is the kinetic energy at the top

is the potential energy at the top

is the kinetic energy at the bottom

is the potential energy at the bottom

The kinetic energy is the energy due to motion; since the train is at rest at the top, we have

Also, at the bottom the height is zero, so the potential energy is zero

Therefore, we find:

13)

The kinetic energy of an object is the energy of the object due to its motion. Mathematically, it is given by

where

m is the mass of the object

v is the speed of the object

From question 12), we know that the kinetic energy of the train at the bottom is

We also know that the mass is

m = 8325 kg

Therefore, we can calculate the speed of the train at the bottom:

14)

At the top of the second hill, the total mechanical energy of the train is still conserved.

Therefore, we can write again:

where

is the kinetic energy at the top of the 1st hill

is the potential energy at the top of the 1st hill

is the kinetic energy at the top of the 2nd hill

is the potential energy at the top of the 2nd hill

From the previous questions, we know that

and

The height of the second hill is

h = 39 m

So we can also find the potential energy at the second hill:

So, the kinetic energy at the second hill is

And so, the speed is

it is very well related to a lot of things but with my limited knowledge i can confidently say that the answer is space.