Transcript f - Michigan State University

PHYSICS 231
Lecture 8: Forces, forces & examples
Remco Zegers
Walk-in hour: Monday 9:15-10:15 helproom
PHY 231
1
Newton’s Laws
 First Law: If the net force exerted on an object
is zero the object continues in its original state of
motion; if it was at rest, it remains at rest. If it
was moving with a certain velocity, it will keep on
moving with the same velocity.
 Second Law: The acceleration of an object is
proportional to the net force acting on it, and
inversely proportional to its mass: F=ma
 If two objects interact, the force exerted by the
first object on the second is equal but opposite in
direction to the force exerted by the second
object on the first: F12=-F21
PHY 231
2
Forces seen in the previous lecture
• Gravity: Force between massive objects
• Normal force: Elasticity force from supporting surface
n=-FgL
FgL=mgcos 
Fg//=mgsin
Fg=mg 
PHY 231
3
Gravity, mass and weights.
Weight=mass times gravitational acceleration
Fg(N)=M(kg) g(m/s2)
Newton’s law of universal gravitation:
Fgravitation=Gm1m2/r2
G=6.67·10-11 Nm2/kg2
For objects on the surface of the earth:
•m1=mearth=fixed
•r=“radius” of earth=fixed
•The earth is not a point object relative to m2
PHY 231
4
Jumping!
The pelvis has a mass of 30.0 kg. What
is its acceleration and direction of
acceleration?
PHY 231
5
Tension
T
The magnitude of the force T
acting on the crate, is the same
as the tension in the rope.
Spring-scale
You could measure the tension by inserting
a spring-scale...
PHY 231
6
question
ceiling
A block of mass M is hanging
from a string. What is the
tension in the string?
M
a)
b)
c)
d)
e)
T=0
T=Mg with g=9.81 m/s2
T=0 near the ceiling and T=Mg near the block
T=M
one cannot tell
PHY 231
7
Newton’s second law and tension
m1
No friction.
What is the acceleration of
the objects?
m2
PHY 231
8
Problem
What is the tension in the string and
what will be the acceleration of the
two masses?
PHY 231
9
Friction
Friction are the forces acting on an object due to interaction
with the surroundings (air-friction, ground-friction etc).
Two variants:
• Static Friction: as long as an external force (F) trying to
make an object move is smaller than fs,max, the static
friction fs equals F but is pointing in the opposite direction:
no movement!
fs,max=sn s=coefficient of static friction
• Kinetic Friction: After F has surpassed fs,max, the object
starts moving but there is still friction. However, the
friction will be less than fs,max!
fk=kn k=coefficient of kinetic friction
PHY 231
10
PHY 231
11
friction
20 kg
pull
A person wants to drag a crate
of 20 kg over the floor. If he pulls
the crate with a force of 98 N,
the crate starts to move. What
is s?
After the crate starts moving, the person continues to
pull with the same force. Given k=0.4, what is the
acceleration of the crate?
PHY 231
12
General strategy
• If not given, make a drawing of the problem.
• Put all the relevant forces in the drawing, object by
object.
• Think about the axis
• Think about the signs
• Decompose the forces in direction parallel to the
motion and perpendicular to it.
• Write down Newton’s first law for forces in the
parallel direction and perpendicular direction.
• Solve for the unknowns.
• Check whether your answer makes sense.
PHY 231
13
What about…
A heavy-duty SUV and small car collide. Is the force of
the SUV on the small car:
a)
b)
c)
d)
greater than the force of the small car on the SUV
smaller than the force of the small car on the SUV
the same as the force of the small car on the SUV
It is impossible to say
PHY 231
14