22 their connection with space and time properties

Theoretical material

Conservation law, also called law of conservation, in physics, several principles that state that certain physical properties (i.e., measurable quantities) do not change in the course of time within an isolated physical system. In classical physics, laws of this type govern energy, momentum, angular momentum, mass, and electric charge. In particle physics, other conservation laws apply to properties of subatomic particles that are invariant during interactions. An important function of conservation laws is that they make it possible to predict the macroscopic behaviour of a system without having to consider the microscopic details of the course of a physical process or chemical reaction.

The momentum of an isolated system is a constant. The vector sum of the momenta mv of all the objects of a system cannot be changed by interactions within the system. This puts a strong constraint on the types of motions which can occur in an isolated system. If one part of the system is given a momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same momentum in the opposite direction. As far as we can tell, conservation of momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.

Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle. One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated system remains constant.

The angular momentum of an isolated system remains constant in both magnitude and direction. The angular momentum is defined as the product of the moment of inertia I and the angular velocity. The angular momentum is a vector quantity and the vector sum of the angular momenta of the parts of an isolated system is constant. This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction. As far as we can tell, conservation of angular momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.

Answers for solving problems (past papers)

Q1) D

Q2) B

Q3) B

Q4) C

Q5) B

Q6) B

Additional problems and tasks

1)      Ball A, with a mass of 2 kg, moves with a velocity 5 m/s. It collides with a stationary ball B, with a mass of 4 kg. After the collision, ball A moves in a direction 60.0 degrees to the left of its original direction, while ball B moves in a direction 50.0 degrees to the right of ball A's original direction. Calculate the velocities of each ball after the collision.

2)      A man drops a 10 kg rock from the top of a ladder of height 5 m.

What is its speed just before it hits the ground?

What is its Kinetic Energy when it reaches the ground?

3)      The diagram below shows a 10,000 kg bus traveling on a straight road which rises and falls. The horizontal dimension has been foreshortened. The speed of the bus at point A is 26.82 m/s (60 mph). The engine has been disengaged and the bus is coasting. Friction and air resistance are assumed negligible. The numbers on the left show the altitude above sea level in meters. The letters A–F correspond to points on the road at these altitudes.

Find the speed of the bus at point B.

An extortionist has planted a bomb on the bus. If the speed of the bus falls below 22.35 m/s (50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If you feel the bus will explode, identify the interval in which this occurs.

Derive an equation to determine the speed of the bus at any altitude.

4)      A ball is dropped from the top of a tall building and reaches terminal velocity as it falls. (At terminal velocity drag equals weight and a falling object stops accelerating.) Will the potential energy of the ball upon release equal the kinetic energy it has when striking the ground? Explain your reasoning.

5)      A 55 kg human cannonball is shot out the mouth of a 4.5 m cannon with a speed of 18 m/s at an angle of 60°. (Friction and air resistance are negligible in this problem. You may not use Newton's laws or the equations of motion to solve these problems. Think conservation of energy.) Determine the following quantities for the human cannonball she exits the mouth of the cannon…

the horizontal and vertical components of her velocity

her kinetic energy

Determine the following quantities for the human cannonball at the top of her trajectory.

the horizontal and vertical components of her velocity

her kinetic energy

her potential energy relative to the mouth of the cannon

her height above the mouth of the cannon

6)      A laboratory cart (m1 = 500 g) is pulled horizontally across a level track by a lead weight (m2 = 25 g) suspended vertically off the end of a pulley as shown in the diagram below. (Assume the string and pulley contribute negligible mass to the system and that friction is kept low enough to be ignored.)

If the lead weight falls 85 cm, determine…

the final speed of the system

the acceleration of the system

the tension in the string

7)      A 1200 kg car driving downhill goes from an altitude of 70 m to 40 m above sea level and accelerates from 11 m/s to 23 m/s.

How much potential energy did the car lose?

How much kinetic energy did it gain?

How much energy is unaccounted for?

Where did this energy go?