Systems, Impact and Energy Systems

Question 1

The principle of linear momentum states that the ____ __________ __ ___ ________ __ ___ _____ ___ is equal to the resultant of the external forces acting upon the system

Answer 1

Principle of linear momentum states that the time derivative of the
momentum of the whole system is equal to the resultant of the
external forces acting upon the system

Question 2

What is the overall momentum of a system of particles?

Answer 2

H = Mv(c)
Momentum of system = Mass of system * Velocity of the mass centre

Question 3

What is the angular momentum of a system of particles about a point?

Answer 3

K = ∑ r x mv

Question 4

What is the relationship between angular momentum and momentum?

Answer 4

The time derivative of the angular momentum is equal to the momentum

Question 5

During impact, what are the names of the two periods?

Answer 5

• Period of deformation
• Period of restitution

Question 6

What is the total impulse after impact?

Answer 6

0

Question 7

What is the momentum before and after impact?

Answer 7

mv1 + mv2 = mv’1 + mv’2

Question 8

What is the coefficient of restitution?

Answer 8

This is the ratio of the deformation impulse and the restoration impulse
e = Restoration Impulse / Deformation Impulse

Question 9

What does a coefficient of restitution of 1 represent?

Answer 9

A perfectly elastic collision

Question 10

What can impact the coefficient of restitution?

Answer 10

• Material Used
• Relative Velocity Impact

Question 11

What types of impact are there?

Answer 11

• Direct Central Impact:
  Mass centres of bodies are on the line of impact and velocities are also directed along the line of impact
• Direct Oblique Impact:
  Mass centres of bodies are on the line of impact but velocities aren’t directed along the line of impact
• Eccentric Impact:
  Mass centres aren’t on the line of impact

Question 12

What is the coefficient of restitution relative to the velocities before and after impact?

Answer 12

e = (v’2 - v’1) / (v1 - v2)

Question 13

What is the energy loss after an impact?

Answer 13

1/2 * (1 - e^2) * ((m1 * m2) / (m1 + m2)) * (v1 - v2)^2

Question 14

How do you calculate the velocities of an oblique central impact?

Answer 14

We need to resolve the velocities so then they are on the line of impact by using trigonometry. Then we can use the same principles as a direct central impact

Question 15

What is the kinetic energy of a system equal to?

Answer 15

The sum between the kinetic energy in a translation with the velocity of the mass centre and the kinetic energy of the particles in their rotation about the mass centre