PHYSICS 231 Lecture 8: Forces, forces

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PHYSICS 231Lecture 8 Forces, forces examples

• Remco Zegers
• Walk-in hour Monday 1130-1330
• Helproom

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Newtons 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 Fma
• 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

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Forces seen in the previous lecture

• Gravity Force between massive objects
• Normal force Elasticity force from supporting
  surface

?
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Gravity, mass and weights.

• Weightmass times gravitational acceleration
• Fg(N)M(kg) g(m/s2)
• Newtons law of universal gravitation
• FgravitationGm1m2/r2
• G6.6710-11 Nm2/kg2
• For objects on the surface of the earth
• m1mearthfixed
• rradius of earthfixed
• The earth is not a point object relative to m2

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Measuring mass and weight.
Given that gearth9.81 m/s2, gsun274 m/s2,
gmoon1.67 m/s2, what is the mass of a person on
the sun and moon if his mass on earth is 70 kg?
And what is his weight on each of the three
surfaces?

• The mass is the same on each of the surfaces

• On Earth w686.7 N
• On the Moon w116.7 N
• On the Sun 19180 N

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Jumping!
The pelvis has a mass of 30.0 kg. What is its
acceleration?
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Tension
The magnitude of the force T acting on the crate,
is the same as the tension in the rope.
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Newtons second law and tension
m1
No friction.
What is the acceleration of the objects?
m2
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Problem
What is the tension in the string and what will
be the acceleration of the two masses?
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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 ?scoefficient 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 ?kcoefficient of kinetic friction

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Problem
A)If ?s1.0, what is the angle ? for which
the block just starts to slide? B)The block
starts moving. Given that ?k0.5, what is
the acceleration of the block?
A) Parallel direction mgsin?-?sn0 (?Fma)
Perpendicular direction mgcos?-n0 so nmgcos?
Combine mgsin?-?smgcos?0
?ssin?/cos?tan?1 so ?45o
B) Parallel direction mgsin(45o)-
?smgcos(45o)ma (?Fma) g(½?2-¼?2)a so
ag¼?2
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All the forces come together...
If a3.30 m/s2 (the 12kg block is moving
downward), what is the value of ?k?
For the 7 kg block parallel to the
slope T-mgsin?-?kmgcos?ma For the 12 kg block
Mg-TMa
Solve for ?k
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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 Newtons first law for forces in the
  parallel direction and perpendicular direction.
• Solve for the unknowns.
• Check whether your answer makes sense.

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Next Lecture
Revision and go through an exam
May the Force be with you!