Transcript Newton`s 2nd law problems

Newton’s 2nd law problems
ΣF = ma
Or
F net = ma
F = ma
• Determine the acceleration which result
when a 12-N net force is applied to a 3-kg
object and then to a 6-kg object.
A)
b)
F = 12 N
F = 12 N
m = 3 kg
m = 6 kg
12 = 3a
12 = 6a
A = 4 m/s2
a = 2 m/s2
• A man is pulling a cart (total 8.7 kg) with a
force of 168 N. Neglecting friction, how
much time does it take to get the cart from
rest up to 8 m/s?
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m = 8.7 kg
F = 168 N
Vo = 0 m/s
V = 8 m/s
t= ?
Need to find acceleration first,
F = ma
168 = 8.7a
A = 19.3 m/s2
then solve acceleration for time
a = (v-vo)/ t t = (v-vo) /a
(8-0)/19.3 = 0.41 sec
ΣF = all the forces that are acting on that
one object in the same plane added
together.
• More than one force can act on an object at once.
• For example, two people could push on a book at the
same time. One person could push toward the left and
the other could push toward the right. In this case the
two forces would act against each other.
– If the force toward the left was greater than the force toward the
right, then the prevailing force would be toward the left. The
strength of this prevailing force would be the difference between
the strengths of the two separate forces. In this prevailing force
is called the net force. Basically, the word net means total.
• For example, if one person
pushed the book with a
force of 20 Newtons toward
the left, and the other
person pushed the book
with a force of 18 Newtons
toward the right, then that
the net force would be 2
Newtons in size and
directed toward the left.
– As you can see, the net force
is aimed toward the left. This
object will move as if it had a
single force of 2 Newtons
pushing on it toward the left.
• Forces which are aimed to the right are usually
called positive forces.
• And forces which are aimed to the left are
usually said to be in a negative direction.
– So, to be more accurate, in the above diagram we
should call F1 a negative force, that is, negative 20
Newtons, and we should call F2 a positive force, or
positive 18 Newtons.
• Since the net force is aimed to the left; it is a
negative force. Thus, Fnet = -2N
If an object is not moving, are there
any forces acting on it?
• Yes
– No movement means the sum of the Forces =
0 N.
– Example: an object resting on the table.
• The forces acting are:
– The object pushing down on the table
– The table pushing up on the object.
– Neither of these forces act to cause any motion
What does it mean for an object to
be moving at a constant speed?
• This means that there is no acceleration.
• This means that the sum of the forces
acting on that object add up to zero.
• Weight = mg
• T or Ft = tension
• ΣF = T - mg = ma if something is pulling
up and the weight is pulling down.
• Don’t forget other motion formulas such as
V2 = vo2 + 2ad
y = yo + vot + ½ at2
Decide which way is the motion and
therefore the +y, and the acceleration.