Chapter 5. Applying Newton’s Laws. Goals for Chapter 5. To use and apply Newton’s First Law To use and apply Newton’s Second Law To study friction and fluid resistance To consider forces in circular motion. Introduction.
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Applying Newton’s Laws
Engine:T1 = w
T3 = 1.155w
T2 = 0.577w
Block and cart: w2=0.26w1
Caution: ma doesn’t belong in free-body diagrams.
Fw = 300 N
Fw = 400 N
T = 9440 N
n = 390 N
a = g sinα
n = mg cosα
a = 6.0 m/s2
F T on C = 3.0 N
Sometimes, you need to combine both approaches to solve a problem
The friction and normal forces are really components of a single contact force.
μkis a constant called the coefficient of kinetic friction. μkdepends on the types of surface. Because it is a ratio of two force magnitudes, μkis a pure number, without units.
The equation is only an approximate representation of a complex phenomenon. As a box slides over the floor, bonds between the two surfaces form and break, and the total number of such bonds varies; hence the kinetic friction force is not perfectly constant.
Both equations of friction are relationships between magnitudes, not vector relationships.
T = 188 N
The tension required is less.
n = 406 N
Fluid resistance at low speed
Where k is a proportionality constant that depends on the shape and size of the body and the properties of the fluid. The unit of k is N∙s/m or kg/s
Fluid resistance at high speed
The value of D depends on the shape and size of the body and on the density of the air. The units of the constant D are N∙s2/m2 or kg/m
∑Fy = mg + (-Dvy2) = may
vt= 44 m/s