6.2 Mechanical Energy

6.2 Mechanical Energy

Work-Energy Theorem

• States that the work done on a system is equal to the sum of the changes in kinetic and potential energies of the system

• W = ΔE_k + ΔE_p

• ΔE_k If the work is done by an unbalanced force (non-zero net Force), the object will accelerate, according to Newton's 2d law. When an object increases its speed, it gains kinetic energy

• ΔE_p An object an gain gravitational potential energy and/or elastic potential energy as a result of work being done on it

W = Fd

The force exerted by the engine causes the displacement of the rocket, therefore work is done on the rocket

Ep = ugh

The rocket experienced a change in height relative to the ground, therefore it gained gravitational potential energy

Work-Energy Theorem

The amount of work done on an object is equal to the sum of the change in potential and kinetic energies

ΔEk = W - ΔEp

Ek = 1/2mv²

Use the kinetic energy and mass to solve for the speed of the rocket

Calculations of Mechanical Energy

The mechanical energy of an object is equal to the sum of its kinetic energy and all forms of potential energy
 $E_m=E_k+\ E_p$  

Multiple Choice

A 7.40 kg cannonball is fired from the Earth's surface and has 29.5 kJ of mechanical energy when it is moving at 85.0 m/s. What is the kinetic energy of the cannonball at that point?

• 26.7 kJ

• 29.5 kJ

• 53.5 kJ

• 56.2 kJ

Ek = 1/2mv²

Use the mass and the speed of the cannonball to find the kinetic energy.

Open Ended

A 7.40 kg cannonball is fired from the Earth's surface and has 29.5 kJ of mechanical energy when it is moving at 85.0 m/s. Determine the cannonball's heigh above the Earth's surface.

Ep = Em - Ek and Ep = mgh

Find the gravitational potential energy from Em and Ek.

Then use the formula for Ep to find the height, h.