Force and Motion – I
Take Quiz 5 Lecture Q&A
Force and Acceleration
Acceleration causes ΔV Force What causes acceleration? Force: an interaction that causes acceleration Kinematics: Study of motion without consideration of force (Describe motion) Mechanics: Study of force and motion (Explain motion)
Newton’s First Law of Motion Law ofInertia
An object with no net force acting on it remains at rest or moves with constant velocity in a straight line.
No net force is needed to keep a constant velocity. A net force is needed to change a velocity.
Net force = 0 Object at Equilibrium. A special case of Second Law of Motion.
Interpretation of Newton’s First Law
If no net force acts on a body, we can always find areference frame in which that body has no acceleration. Inertial Frame of Reference:
– – –
Fnet = 0 on a body, then a = 0 Inertial Frame Fnet = 0 on the frame The frame moves with constant velocity. Inertia: Resistance to force Inertia ≈ Mass for now
Newton’s First Law: Law of Inertia
Newton’s Second Law of Motion
The acceleration of a body is directly proportional to the netforce on it and inversely proportional to its mass.
ΣF ⇔ ΣF = ma a= m
∑F or Fnet: net force, total force, resultant force Force is the cause, and acceleration is the effect. Unit of Force:
F = ma
m [F] = [m] [a] = kg × 2 = Newton = N s
Practice: An experimental rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. What is the magnitude of the requiredaverage force if the sled has a mass of 500 kg.
m km ⎛ 1000m ⎞ ⎛ 1 h ⎞ vi = 0, v f = 1600 ⎟ = 444 , ⎜ ⎟⎜ s h ⎝ km ⎠ ⎝ 3600 s ⎠ Δt = 1.8s, m = 500kg , F = ?
m Δv v f − vi 444. s − 0 m a= = = = 247. 2 Δt 1.8s Δt s
F = ma = 500kg × 247 m / s 2 = 1.24 × 105 N
ΣFx = + all forces in + x direction
Force is a vector.
− all forces in − x direction
⎧ ΣFx = max ⎪ ΣF = ma ⇒ ⎨ ΣFy =ma y ⎪ ⎩ ΣFz = maz
The acceleration component along a given axis is caused only by the sum of the force components along that same axis and not affected by force components along any other axis.
Example: 113-62 Three forces act on a particle that moves with unchanging velocity of v = (2 m/s)i – (7 m/s)j. Two of the forces are F1 = (2N)i + (3N)j + (-2N)k and F2 = (-5N)i + (8N)j + (-2N)k.What is the third force?
ˆ ˆ F1 = (2 N )iˆ + (3N ) ˆ + ( −2 N )k , F2 = ( −5N )iˆ + (8 N ) ˆ + ( −2 N )k , j j v = (2m / s )iˆ − (7m / s ) ˆ = constant, F3 = ? j
v = constant ⇒ ΣF = 0 ⇒ F1 + F2 + F3 = 0
⎧ F3 x = − ( F1x + F2 x ) = − [ 2 N + (−5 N )] = 3N ⎪ ⇒ ⎨ F3 y = − ( F1 y + F2 y ) = − ( 3N + 8 N ) = −11N ⇒ F3 = − ( F1 + F2 ) ⎪F = − ( F1z + F2 z ) = − [ −2 N + (−2 N ) ] = 4 N ⎩ 3z
ˆ ˆ ⎡= − ⎣ ( 2 N − 5 N ) i + ( 3 N + 8 N ) ˆ + ( −2 N − 2 N ) k ⎤ j ⎦
ˆ ˆ F3 = (3N )i − (11N ) ˆ + (4 N )k j
Two kinds of mass
Two methods to measure or use mass
Inertial mass: measure mass by comparing acceleration of this object to acceleration of an object of known mass when the same force applied to both of them.
a0 F = ma = m0 a0 ⇒ m = m0 a
Gravitational mass: measure mass bycomparing gravitational force on this object to gravitational force on an object of known mass at the same location
W W W0 W m0 ⇒ m= W = mg ⇒ g = ⇒ g = = W0 m m0 m
But what exactly is mass?
mass ≠ weight or size intrinsic characteristic how much a body resist to force a characteristic of a body that relates a force on the body to the resulting acceleration of the body
Force Diagram Draw simple diagram Draw all forces acting on the object being considered
Ignore all forces this object acting on other objects Draw forces starting from center of object or at points of action Make sure each force giver can be identified
Free-Body Diagram Example
N: Normal force, force of incline supporting box T: tension, force of person...