ChemPhys 173/273

Unit 11: Work, Energy and Power

Problem Set F

Overview:

Problem Set F consists of six difficult (mostly) and complex problems which test your ability to use the work-energy equation to analyze a physical situation. Like Sets C, D and E, the main equation of importance is

KEi + PEi + Wnc = KEf + PEf

Each term of this equation can be calculated from their respective equations and the stated values of mass (m), speed (v), height (h), spring constant (k), spring compression/stretch distance (x), force (F) and displacement (d).

 KE = 0.5•m•v2 PEgrav = m•g•h PEspring = 0.5•k •x2 Wnc = F•d•cos()

In some instances, the force will be a friction force and will have to be calculated from the coefficient of friction and the normal force (Ffrict = mu•Fnorm). In other instances, the friction will be present on an inclined plane and the normal force will have to be determined by first calculating the perpendicular component of gravity (Fperp = m•g•cos()). In more complicated cases, there will be more than one non-conservative work term. In instances in which an object moves along an inclined plane and then along a horizontal surface, the force of friction is different on the two surfaces; thus a work term for the incline and for the horizontal surface will have to be written separately.

Each problem of the set includes its own unique complications. In one problem, a projectile trajectory is analyzed using energy (rather than the usual kinematics); the horizontal speed at the peak position will have to be equated with the horizontal component of the initial launch velocity. In another problem, trigonometry will have to be used to determine the initial height of a pendulum-like object using the angle of deflection with respect to the vertical. Two problems involve springs, demanding the use of the elastic potential energy equation (above). One problem involves a force exerted downward at an angle in order to accelerate an object across a horizontal surface.

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Work | Sample Work Calculations | Potential Energy | Kinetic Energy | Mechanical Energy

Resolving Fgrav on an Inclined Plane

View Sample Problem Set.

 Problem Description Audio Link 1 Calculation of the final speed of a swinging child if the length of the supporting rope and the angle of deflection are stated. 2 Determination of the stopping distance along a horizontal surface is a block slides down an rough incline and then across the rough surface. 3 Analysis of an angle-launched projectile to determine the peak height. 4 Calculation of the final speed of an object which is accelerated along a rough horizontal surface by a force exerted downward at an angle to the horizontal. 5 Analysis of a mass on a spring to determine the final speed at a certain stretched distance. 6 Determination of the final speed of an object which is launched by a spring-loaded gun across a rough horizontal surface elevated above the ground.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 ||

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