If the cord is subjected to a constant force of F=30 lb and the smooth 10 -lb collar starts from

If the cord is subjected to a constant force of F=30 lb and...

Key Concepts

Ideal Pulley Systems

Ideal pulley systems assume that the pulleys are frictionless and massless, which ensures that the tension in the cord remains constant throughout its length and that there are no losses due to rotational inertia. This simplifies the dynamics of the system by allowing focus on the translational motion of connected objects without additional complications from the pulley's properties.

Work-Energy Principle

The work-energy principle connects the work done by forces to the change in the kinetic energy of an object. In problems where a force does work to accelerate an object from rest, this principle simplifies the analysis by equating the work (force times displacement) to the increase in kinetic energy, making it easier to solve for final speeds without detailed time-dependent acceleration calculations.

Newton’s Second Law

Newton’s second law provides the fundamental relationship between force, mass, and acceleration, expressed as F = ma. It is used to determine how a constant applied force accelerates an object, and forms the basis for further analyses in kinematics, where acceleration contributes to changes in velocity over time or distance.

Transcript

00:01 So in this problem, we have a cord that has a collar in the middle of it, and that collar is being pulled by a pulley with a force of 30 pounds.

00:10 We're also given the weight of this collar, which is 10 pounds, and we can convert this by dividing by 32 .2 feet per second squared, so that we can get the mass of the collar, which is 0 .31 kilograms.

00:28 And now for this problem, we want to find the speed of this collar when it starts from a and then moves all the way to point b.

00:38 So because we're dealing with forces, we want to find the speed of this object.

00:45 We can use the work energy principle, and this relates to the work and the kinetic energy being done on the system.

00:55 And embedded in work is the forces of the system.

00:59 This equation is the initial kinetic energy of the system plus the work being done is equal to the final kinetic energy.

01:13 Now since this object starts at rest, the initial kinetic energy is zero because the initial velocity is zero.

01:24 And of course we can expand the final kinetic energy.

01:28 So for now let's just leave work by itself.

01:31 So the work being done by the system is equal to 1 half.

01:35 M, the mass of the collar, times final velocity squared, which we'll call v2.

01:41 And this is what we're trying to solve.

01:44 So now let's look at the work being done on the system.

01:51 So if you think about it, we have the work being done by this force of the pulley, pushing this collar a certain distance.

02:02 And we also have the weight of the collar.

02:07 Trying to push it back down.

02:09 So the work due to the weight is going in the opposite direction of the work done by the pulley...

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