3.6 Problem Solving

Mechanical

Up to this point, we've considered energy in a great variety of forms.

For our calculations, we're going to mainly focus on "mechanical" forms of energy.

Mechanical forms of energy include kinetic energy and potential energy (with work used to involve forces adding or removing energy from a system).

Being able to calculate both of these, allows us to solve a wide variety of energy conservation problems.  

Here's the general concept we'll be looking at - conversions between E_k and E_p and back to E_k.

Conservation of Energy

The Law of Conservation of Energy states energy cannot be created or destroyed. This law is elegant and can be used to solve an unknown in a problem. 

E_before = E_after

Because we're focusing on mechanical energy, let's include Ep and Ek.   We'll also include Eh, as we'll sometimes need to determine lost energy.

Where:

Dropped Rock Example

Here's a simple one to start with. Test your knowledge by trying the problem below.

Example:
A 1.6 kg rock is dropped from a height of 15 m. With what speed will it strike the ground. Ignore air resistance. Solve using conservation of energy (start with E_before = E_after).




Answer: 17 m/s

Solution

Thrown Ball Example

Test your knowledge by trying the problem below.

Example:
A ball is thrown straight up leaving the player's hands at at 6.0 m/s. If air resistance is ignored, how high can the ball travel?



Answer: 1.8 m

Solution

Pole Vaulting

Let's consider the energy transfers used in a pole vault.

Broken down into three main steps to reach a height that'll get you over the bar.

A. Sprint	B. Plant Pole and Bend	C. Spring Over Bar

Test your knowledge by trying the problem below.

Skier Example

Test your knowledge by trying the problem below.

Example:
A skier starts from rest at the top of a frictionless incline of height 20 m as shown here. How fast is the skier travelling at the bottom of the hill?




Answer: 20 m/s

Solution

Pendulum

Test your knowledge by trying the problem below.

Example:
Professor Lewin releases the ball from his chin (h = 1.8m).
a) If he ensures that the ball has zero motion when released from position A, what would be the ball's velocity at point B?
b) How high would the ball go on the other side (assuming no energy lost to heat)?
c) Since it WILL lose a tiny bit of energy, what do you know about the maximum heights each swing?
d) How can professor Lewin be so confident that he won't be going to the hospital?
e) Why was he SO careful about how he released the ball?

Answer: 5.9m/s, 1.8m

Solution

Rope Swing Example

Pendulums are popular energy problems. Test your knowledge by trying the problem below.

Example:
A girl runs at top speed (5.0 m/s) and grasps a 4.0 m rope hanging vertically from a tall tree at the edge of a lake.
a) how high can she swing upward?
b) does her mass affect the answer?
c) does the length of the vine affect the answer?




Answer: 1.3 m

Solution

Roller Coaster

A roller coaster ride is a thrilling experience which involves a lot of physics. A great tool for the analysis of a roller coaster is the conservation of energy.

Once the cars are lifted to the top of the hill, gravity takes over and the remainder of the ride is an experience in energy transformation.

As the cars descend they lose much of this initial potential energy (as they lose height). While losing potential energy, the cars subsequently gain kinetic energy. 

Test your knowledge by trying the problem below (assume no heat loss).

Skate Park Simulation

Try out the simulation below.   You'll be asked some related questions in your Learning Guide.

Interview

What do physicists, technologists, and engineers do? Here's an example.