forces contact forces - those resulting from physical contact between objects –normal force...
TRANSCRIPT
Forces
• Contact Forces - those resulting from physical contact between objects
– Normal Force
– Friction
– Tension (spring/rope)
– Compression
• Action at a Distance Force - Field Forces
– Gravity
– Electromagnetic
– Strong Nuclear Force• Holds Nucleus Together
– Weak Nuclear Force• Decay Process
•Force - The capacity to cause physical change in the motion of an object.
Newton’s First Law – Law of Inertia
• An object at rest will remain at rest – and an object in motion will continue in motion at a
constant velocity (Magnitude and Direction)– unless acted upon by a nonzero net external force.
• Inertia – The tendency of a body to maintain its state of rest or constant velocity.
• Equilibrium - A condition during which the velocity of an object is constant or the object is at rest. The net force acting on the object is zero.
• Inertial Reference Frame – Place where Newton's Laws are valid. (at rest or constant velocity)– Non-inertial reference frames are accelerating.
Weight and Mass
• Mass - A term used to quantify/measure inertia.
– Has SI units of kilogram.
– The amount of a substance.
– The quantity of matter.
– Scalar
• Weight - Force exerted on an object while it is under the influence of a gravitational field.
– Vector
• Density - The amount of a substance per unit volume.
Newton’s Second Law
• The acceleration of an object is – directly proportional to the net force acting on it – and inversely proportional to its mass.– The direction of the acceleration is in the
direction of the net force acting on the object.
Fa
m
F vector sum of all forces
F ma
Units
PhysicalQuantity
DimensionSymbol
SI MKS SI CGS USCustomary
Length [L] m cm ft
Mass [M] kg g slug
Time [T] sec sec sec
Acceleration [L/T2] m/s2 cm/s2 ft/s2
Force [M-L/T2] newton (N)kg-m/s2
dyneg-cm/s2
pound (lb)slug- ft/s2
1 lb 4.45 N
Alternate Statement of the Second Law
• Momentum - The quantity of an object’s motion. The product of an object’s mass and velocity.
• The time rate of change of the momentum of an object is equal to the resulting net external force acting on the object.
p mv
dpF
dt
Weight and Mass
• Mass - A term used to quantify/measure inertia.
– Has SI units of kilogram.
– The amount of a substance.
– The quantity of matter.
– Scalar
• Weight - Force exerted on an object while it is under the influence of a gravitational field.
– Vector
• Density - The amount of a substance per unit volume.
GˆF mg mgj
Example 1
• What constant net force must be used to bring a 1500 kg car to rest from a speed of 100 km/hr within a distance of 55 m?
Newton’s Third Law
• If two objects interact (contact or at a distance),
• the force exerted on body 1 by body 2 (F12)
• is equal and opposite the force exerted on body 2 by body 1 (- F21 ).
On By
Cautions on the Third Law
• The forces of an action-reaction pair always act on different bodies. They do not combine to give a net force and cannot cancel each other.
Model Assumptions
• Surfaces are frictionless (*)• The mass of a rope or string is zero.• The tension in a rope is the same everywhere in
the rope. (The force(s) it exerts is(are) on the object(s) it is attached to).
• Ropes are non-extensive (do not get longer)• A pulley has no friction or mass (*). It simply
redirects the tension in another direction.
Problem Solving Approach• Read the problem. Several times if necessary.
• Write down the information that is given or looked up in a table.
• Write down what is to be found.
• Draw a picture or sketch. Draw and label with forces, velocities, accelerations, etc. Isolate the object(s) of interest.– Free body diagram.
– Specify your coordinate system.
– Resolve forces along these coodinate axes.
• Write down the fundamental relationships/definitions/formula you need to solve the problem.– Apply Newton’s laws in component form along coordinate axes.
• Manipulate the equations. # Equations = # Unknowns.
• Check that your answer makes sense.
• Actually plug in numbers at the very end. Include unit analysis.
• Box your final answer. Include units and check for significant digits.
Big Picture
• If the object is at rest or moving at a constant velocity it is in equilibrium and the 1st Law applies.
• If the the forces don’t seem balanced the object will accelerate and the second law applies
F 0
F ma
Example 2
• A 10 kg box is sitting on the table.
• You pull up with a string attached to the box and apply 40 N.
• What is the normal force applied by the table on the box?
Example 3
• Two boxes are connected by a cord and pulled by a second cord attached to the first box with a force of 40.0 N
• The two boxes have masses of 12.0 kg and 10.0 kg as shown.
• Find the acceleration of each box and the tension in the cord
Resolve into components
mg
1 21T
2T
mg
2 2T sin
2 2T cos
1 1T sin
1 1T cos
1 1y 2 2T sin T nF mi0 gs 1x 2 21T cos TF 0 cos
Atwood’s Machine (a pulley)
Object 1: Elevator Car
y T 1 1F F m g m a
Object 2: Counterweight
y T 2 2F F m g m a
Incline plane (no friction)
• m2 = 7 kg• Which way do
blocks move?• What is
acceleration?• What is tension
in cord?