How to Solve Physics Problems in 5-Steps
In spite of the diversity of physics problems, there are some general approaches
that can be applied to a multitude of circumstances. The following two-part
problem, which involves multiple forces acting upon an object is used to
illustrate an iteration of some basic techniques.
1. What is the acceleration of a 120kg object sliding down a frictionless incline at an angle of 30 degrees? 2.What is the normal force acting upon the object?
STEP 1. Read the problem carefully
STEP 3. Decompose forces along these coordinate axes Attempt to resolve each force into vector components along the coordinate axes, the normal force is perpendicular to the motion, however one must recognize the vertical force of gravity must be proportional to the incline angle θ. STEP 4. Apply Newton’s Second Law to each component Apply Newton's Second Law to each of the components. The law states that the sum of the forces acting upon a body is equal to the product of its mass and acceleration. where, F is the sum of all external forces acting upon the object of mass m and a is the acceleration resulting from that force. Resolving this equation into components yields:
Fx = max
ay must equal zero given that the object does not move in a direction perpendicular
to the incline surface. Now recall that we are trying to find ax – the
acceleration of the object down the incline. In the direction perpendicular to
the incline there is both a component of gravity and the normal force of the
incline.
Fx = -mg sinθ = max
-mg sinθ = max ⇒ ax = -g sinθ
The acceleration of the object down the incline, and the normal force on the
object are therefore:
ax = -g sinθ =(9.8m/s2)(sin30o) = 4.9m/s2
Compare your initial estimate and check that the units are correct. The
acceleration of 4.9m/s2 compares well to our estimate of 3m/s2, and we’ve
indicated the SI units of force correctly.
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