In the action adventure film Indiana Jones and the Raiders of the Lost Ark, Indiana Jones searches for the Ark of the Covenant. In one well-known nail biting scene Indiana tries to escape being crushed by a huge boulder rolling down a sloping terrain inside a tunnel. The rolling boulder of mass m rolls down the only path that Indiana Jones can take. Assume that the friction force between the sphere and the surface of the hill is negligible. At a particular time t1 the spherical boulder is at location 1 and moving with velocity v1. At a later time t2 the sphere is at location 2 and moving with velocity v2. Locations 1 and 2 are at vertical heights h1 and h2 respectively, from the bottom of the tunnel. When answering the following questions use 1 and 2 for subscripts to identify the different variables at the two different locations.

Part (a): U ₁ = mgh ₁

Part (b): What is the equation for translational kenetic energy, K _T , ₁ of the spherical boulder?

K _T,1 = .5mv ₁ ²

Part (c): What is the equation for the rotational kinetic energy K _R,1 of the spherical boulder?

K _R,1 = .5 w ₁ ² ; K _R,1 = (1/5)mv ₁ ²

Part (d): What is the equation for the total kinetic energy K _total,1 of the spherical boulder in terms of its linear speed?

K _total,1 = (7/10)mv ₁ ²

Part (e):

You can write a similar expression for the potential energy U ₂ and the total kinetic energy K _total,2 of the spherical boulder when it is at location 2.

A reasonable choice for the initial location 1 would be the point where the spherical boulder starts from rest; i.e. where the sphere has zero initial velocity.

Use this fact and your answers to parts (a), (b), (c), and (d) to write the mathematical equation for the conservation of mechanical energy in terms of the mass, velocity, height and g . Keep the kinetic energy terms on the left and the potential energy terms on the right. Include only non-zero terms. (Use any variable or symbol stated above along with the following as necessary: g .)