Teaching Physics with the Physics Suite Edward F. Redish Problems Sorted by Type | Problems Sorted by Subject | Problems Sorted by Chapter in UP

What's conserved?

In a variety of mechanical dynamic systems, a conservation law such as momentum or mechanical energy applies to an object or set of objects. The conservation law then allows us to put constraints on the system and sometimes to explicitly determine otherwise unknown quantities. A critical element of using conservation laws is in determining when they apply and to what objects. In this problem, we focus on determining the applicability of (mechanical) energy and momentum conservation rather than on using the principles to calculate something.

a. Briefly state and describe the law of conservation of momentum, being careful to define any terms or symbols you use and state the conditions under which it holds. Describe how the law is related to Newton's laws.

b. Briefly state and describe the law of conservation of mechanical energy, being careful to define any terms or symbols you use and state the conditions under which it holds. Describe how the law is related to Newton's laws.

c. For the objects or set of objects described in the numbered list below, complete the following:

• For each object in the set, draw a free-body diagram identifying the forces acting on the object.
• For each force in your free-body diagram, identify whether the force is internal or external to the set. (A force is internal if both the objects causing the force and feeling the force are a member of the set.)
• For each force in your free-body diagram, identify whether the force is conservative or non-conservative. (A force is non-conservative if the changes it causes in the energies of the objects it acts on are not reversible.)
• Identify whether the objects in your system can be considered to conserve momentum and/or mechanical energy for the time interval described.
 1 Object = ball thrown straight upward. Consider the object after it has left the hand but may be rising or falling but has not yet been caught. Ignore the effect of air resistance. 2 Object = block sliding on a smooth table after being pushed but before it comes to a stop. (Smooth ≠ frictionless!) 3 Objects = a car and a truck rolling (in neutral) and smashing into each other, doing damage to each vehicle. Friction with the ground can be neglected. Consider from just before the objects collide to just after they collide. 4 Objects = a heavy cylinder (A) with frictionless wheels rolling along on a horizontal table top and a lighter cylinder (B) that is lightly dropped onto the moving cylinder. Consider the time from just before B lands on A until a bit later when they are rolling together, both at the same speed. 5 Object = an aircart on an incline with a spring on the bottom. The cart slides up and down the incline, bouncing off the spring when it hits the bottom.