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Ch 6 MOMENTUM
Relationship between Momentum & Force
Momentum is the tendency of an object to keep moving with the same speed in the same direction and is a vector quantity (both magnitude and direction).
p = momentum (kg m s
-1
) m = mass (kg) v = velocity (m s
-1
) If an object undergoes a momentum change a net force has to be acting on the object.
∆
p = change in momentum (kg m s
-1
) P
f
= Final momentum (kg m s
-1
) P
i
= Initial momentum (kg m s
-1
)
∆
p = change in momentum (kg m s
-1
) I = Impulse (Ns)
∆
t = contact time (s) If the force is not constant, the impulse affecting an object can be found by calculating the area under a force-time graph.
Conversation of Momentum
The law of conservation of momentum states that in any collision between two or more objects in an isolated system the total momentum of the system will remain constant.
=
∑P
i
= Initial momentum (kg m s
-1
)
∑P
f
= Final momentum (kg m s
-1
)
+
=
+
m
1
m
2
= mass of objects (kg)
u
1
u
2
= initial velocity of objects (m s
-1
)
v
1
v
2
= final velocity of objects (m s
-1
)
Work
Work done on an object is when the energy of the object changes. To do work on an object there needs to be force acting and the object must move (displacement). 1 Joule is equal to work done when 1 Newton acts over 1 metre.
w = work done (J) F = force (N) x = displacement (m)
= angle between the applied force and direction of motion (
o
) Friction acts to slow down the
object →
. No work is done if the force is acting at 90
o
to direction of motion.
Mechanical Energy
Mechanical energy is defined as the energy that a body possesses due to its position or motion.
K
E
= Kinetic energy (J) m = mass (kg) v = speed (m s
-1
)
P
E
= Kinetic energy (J) m = mass (kg) g = gravity (9.8 m s
-2
)
= change in height (m) Elastic Potential energy is stored when a spring is stretched or a elastic material is deformed.
Hooke’s Law states that the force
applied by a spring is directly proportional, but opposite in
direction to the spring’s
extension.
F = Force (N) k = spring constant (m s
-1
)
∆
x = extension or compression length (m) All springs that obey Hooke
’s law
are linear in a force-extension graph, and the gradient is the stiffness constant. The elastic potential energy can be found by the area below a force-extension graph.
= Force (N) k = spring constant (m s
-1
)
∆
x = extension or compression length (m)
Energy Transformation & Power
Isolated system
–
no external forces or energy losses. Total mechanical energy is constant / conserved in an isolated system.
M
ET
= Total mechanical energy (J) K
E
= Kinetic energy (J) P
E
= Potential energy (J)
√
v = velocity (m s
-1
) K
E
= Kinetic energy (J) m = mass (kg) Power is the rate at which energy is used.
P = power (W) W = work (J)
= change in time (s) If work done to overcome friction with no increase in speed is...
P = power (W) F
av
= average force (N)
v
av
= average speed (m s
-1
)
Conversions
km/h
÷3.6
m/s

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