Further Mechanics

Question 1

define momentum

Answer 1

the product of mass and velocity of an object

Question 2

step by step how to solve momentum 2D question

Answer 2

1. read the problem to identify the objects involved. mass, velocity and the angles
2. Break down the components (x and y components)
3. apply conservation of momentum
   sum of momenta in x = sum of final momenta in the x direction)
   sum of momenta in y = sum of final momenta in the y direction)
4. write down the conservation of momentum equations for both the x and y directions
5. solve the system of equations simultaneously to find the unknown quantities

Question 3

what is the kinetic energy equation linking to momentum

Answer 3

Ke = p^2
—————-
2m

Question 4

what is impulse

Answer 4

is equal to the rate of change of momentum

Question 5

state the equation used to calculate the impulse of a force acting over a time

Answer 5

impulse = F x time

Question 6

If there a fixed change of momentum that must occur, how do you reduce the force that is exerted in the process

Answer 6

increase the length of time over which the change of momentum occurs

Question 7

what is the conservation of linear momentum

Answer 7

the total momentum before an event must be equal to the total momentum after an event, assuming no external forces act.

Question 8

what is the conservation of momentum equation

Answer 8

m1 x v1 = m2 x v2

Question 9

what is an elastic collision

Answer 9

a collision in which kinetic energy is conserved
momentum is also conserved

Question 10

what is an inelastic collision

Answer 10

energy is conserved, but kinetic energy isnt conserved . energy is converted into other forms
momentum is conserved

Question 11

equation used to calculate angular velocity

Answer 11

w = velocity / radius

Question 12

what is the time period of a circular orbit with angular velocity w?

Answer 12

T= 2pi / w

Question 13

what is required for an object to move with a circular motion?

Answer 13

A centripetal force

Question 14

in which direction does a centripetal force act?

Answer 14

perpendicular to the direction of the objects motion, towards the centre of the cirular path

Question 15

what equation is used to calculate a centripetal force

Answer 15

F= mv^2
————–
r
F= mrw^2

Question 16

kinetic energy equation in terms of momentum

Answer 16

E = p^2
——-
2m

Question 17

when can you use this equation

Answer 17

when the force is constant since the impulse is proportional to the force, it is also a vector

Question 18

definition of angular velocity

Answer 18

is the angle through which the radius to this point on the circle turns one second
given in lower case sigma (w)
pis^-1

Question 19

Equation for angular velocity and in terms of frequency

Answer 19

2xpi / T (time period)
2 pi x f

Question 20

equation for linear velocity using angular velocity

Answer 20

V = wx r

Question 21

what is the equation for centripetal acceleration in terms of linear velocity

Answer 21

a = v^2
– —-
r

Question 22

what is the equation for centripetal acceleration in terms of angular velocity

Answer 22

a = r x w^2

Question 23

which direction does centripetal force/ acceleration act towards

Answer 23

the middle of the circle

Question 24

what is the centripetal force equation in terms of linear velocity

Answer 24

F= mv^2
——–
r

Question 25

what is the centripetal force equation in terms of angular velocity

Answer 25

F = m x w^2 x r

Question 26

how do you prove centripetal acceleration ( separate horizontal and vertical)

Answer 26

1. draw a circle and plot A and B on the circle
2. draw lines towords the centre and lines perpindicular to show there velocity
3. seperate the velocities into there horizontal and verticel compponents showing v cos theta and v sin theta
4. workout the verticle acceleration
   a = v - u / t
   v cos theta - v cos theta
   ———————————–
   t
   = o so we ignore it
5. workout the horizontal acceleration
   v sin theta - - v sin theta
   ———————————-
   t
   = 2v sin theta
   ————–
   t
6. w = change in theta
   ———————-
   change in time
   v = wr
   v = change in theta x r / change in time
   change in theta = 2 theta
   v = 2 theta r / t
   t = 2 theta x r
   —————-
   v
7. sub into equation 1
   a = v^2 sin theta
   ——————-
   theta r
8. small angle approximation
   sin theta = theta
9. a = v^2/r
   = w^2 x r

Question 27

how do you prove centripetal acceleration in its second proof ( sim triangles)

Answer 27

Circular Motion Basics:
An object moves in a circle of radius r at constant speed 𝑣

Geometry of Velocity Change:
Change in velocity: Δv = v2 - v1
Time taken: Δt

Geometry of Displacement:
The arc length Δs ≈ vΔt (for small Δt).
Corresponding angle Δθ = Δs / r

Similar Triangles:
Triangle of velocity change and triangle of circular motion are similar:
Δv / v = Δs / r

Solve for Δv:
Δv = v × (Δs / r) = v × (vΔt / r)

Acceleration Definition:
a_c = Δv / Δt = v^2 / r

Key Result:
Centripetal acceleration: a_c = v^2 / r

Question 28

what is the verticle motion equation when at the bottem of the loop

Answer 28

mx v^2
———- = contact - weight
r

Question 29

what is the verticle motion when 1/4 of way into loop (horizontal)

Answer 29

contact F = M x V^2
————
r

Question 30

Verticle motion when at the top of the loop

Answer 30

mxv^2
———- = Contact + weight
r

Question 31

senario - on a bridge what would be the force equation on top of the hill

Answer 31

mv ^2
——— = mg - contact
r