5-Steps to Solving Physics Problems

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 Read the problem through – twice, and try to make an estimate of what might be a rough answer. This step can easily be applied to any physics problem. Take time to understand what you are being asked to find, what information is given and what principles are relevant. In this case the problem asks us to find the acceleration of the object down the incline and we need to make an estimate. Since the acceleration of a vertically falling object is 9.8m/s2 and the object is moving down a 30° slope, a fair estimate would be 3m/s2. STEP 2. Draw a clear diagram Draw a clear diagram, indicate all forces acting upon the object of interest, and label all coordinate axes carefully. The diagram should be simple but detailed enough to represent the important features of the problem; lengths, angles, velocities, etc. It is often helpful to draw a free-body diagram showing all forces acting on the object as detailed below. It is a requirement to draw a free-body diagram of the object whose acceleration is under investigation whenever you apply Newton’s 2nd Law. Free-body diagrams show all forces acting up the object of focus, so for our problem we include the force vectors of gravity and the normal force of the incline against the object. It is sometimes convenient to use coordinate axes that are respectively, parallel and perpendicular to the direction of motion of the object. 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 Fy = may 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. Hence, Fx = -mg sinθ = max Fy = N -mg cosθ = may = 0 STEP 5. Solve the problem Solve the problem while avoiding the substitution of numbers as long as possible. This will result in much less math work on your calculator, diminishing the possibility of mistakes. Do algebraic work first, then substitute near the end of the process. This will also cut down on recopying lengthy numbers and their attached units. -mg sinθ = max ⇒ ax = -g sinθ N -mg cosθ = may = 0 ⇒ N = mg cosθ 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 N = mg cosθ = ((120 kg)(9.8m/s2))cos30o = 1018.4N 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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