Download GENERAL PHYSICS I Math. Edu. Program

GENERAL PHYSICS I
Math. Edu. Program
Yohanes Edi Gunanto
TC - UPH
System of Particles, Collisions
Momentum and Impulse
Quantity of Motion
DEFINITION II Newton’s Principia
• The quantity of motion is the measure of the
same, arising from the velocity and quantity of
matter conjointly.
• The motion of the whole is the sum of the
motions of all the parts; and therefore in a body
double in quantity, with equal velocity, the
motion is double; with twice the velocity, it is
quadruple.
Checkpoint Problem
• Consider two carts, of masses m and 2m, at rest on
an air track. If you push first one cart for 3 s and then
the other for the same length of time, exerting equal
force on each, the momentum of the light cart is
1. four times
2. twice
3. equal to
4. one-half
5. one-quarter the momentum of the heavy cart.
Systems and Conservation of
Momentum
Checkpoint Problem: Choice of
system
• Drop a stone from the top of a high cliff. Consider
the earth and the stone as a system. As the stone
falls, the momentumof the system
•
•
•
•
1. increases in the downward direction.
2. decreases in the downward direction.
3. stays the same.
4. not enough information to decide.
External Forces and Change of
Momentum Vector
• The external force may be zero in one direction
but not others
• The component of the system momentum is
constant in the direction that the external force is
zero
• The component of system momentum is not
constant in a direction in which external force is
not zero
Check point Problem : Acrobat and Clown
• An acrobat of mass mA jumps upwards
off a trampoline with an initial ycomponent of velocity vy,0 = v0. At a
height h0, the acrobat grabs a clown of
mass mB. Assume the acrobat grabs
the clown during a time interval that is
negligibly small.
a) What is the velocity of the acrobat
immediately before grabbing the
clown?
b) What is the velocity of the acrobat
immediately aftergrabbing the clown?
c) How high do the acrobat and clown
rise?
Collision Theory
Collisions
• Any interaction between (usually two) objects
which occurs for short time intervals Δt when
forces of interaction dominate over external
forces.
• Of classical objects like collisions of motor
vehicles.
• Of subatomic particles – collisions allow study
force law.
• Sports, medical injuries, projectiles, etc.
Check point Problem: totally
inelastic collision
• A car of mass mA moving with speed vA1 collides with
another car that has mass mB and is initially at rest.
After the collision the cars stick together. What is the
change in mechanical energy due to the collision?
Particle Collisions: Problem
Solving Strategies
Two Dimensional Collisions:
Momentum Flow Diagram
• Consider a collision between two particles. In the laboratory
reference frame, the ‘incident’ particle with mass m1, is
moving with an initial given velocity v1,0. The second ‘target’
particle is of mass m2 and at rest. After the collision, the first
particle moves off at an angle θ1,f with respect to the initial
direction of motion of the incident particle with a final
velocity v1,f. Particle two moves off at an angle θ2,f with a final
velocity v2,f. Draw a momentum diagram representing this
collision. Answer:
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