A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree bra

A monkey is sitting on a wood plate attached to a rope whose...

Key Concepts

Newton's Laws of Motion

Newton's Laws provide the foundation for analyzing the forces acting on bodies. They describe how forces cause acceleration or maintain equilibrium by balancing out, which is essential when determining whether a system accelerates or remains static.

Tension

Tension is the force transmitted along a rope, cable, or string when it is pulled by forces at either end. In systems with ideal, massless ropes, the tension is typically assumed to be uniform throughout, making it a critical factor in calculating forces in pulley arrangements.

Pulley Systems

Pulley systems utilize wheels and ropes to change the direction of applied forces. They often provide a mechanical advantage by splitting the load among different segments of the rope, allowing for easier lift or movement of heavy objects. Understanding pulley dynamics is key when analyzing problems involving ropes over fixed points.

Mechanical Equilibrium

Mechanical equilibrium occurs when all the forces acting on a system cancel out, resulting in no net acceleration. This concept is fundamental in statics, where analyzing whether the sum of forces (and moments) equals zero helps determine the conditions for stability in any system.

Transcript

00:01 So here we have the mass and essentially we have a rope going over the pulley connected to either side of the wooden plate essentially.

00:14 And the monkey itself is sitting on the iron plate.

00:18 So we have a total mass essentially.

00:20 And we can say that then for part a, we can apply the newton second law in the y direction, of course.

00:29 There isn't any really other direction to analyze.

00:34 And this would be two times the tension minus m g equaling zero.

00:39 And so the tension would simply be equal to m g over two.

00:46 Here for part a we can then solve and say that the tension would be equaling 100 .0 kilograms multiplied by 9 .81 meters per second squared this would all be divided by 2, and t is giving us 490 .5 newtons.

01:10 This would be the minimum force required by the monkey in order for it to just start moving.

01:18 And then once it starts moving, it will then move at a constant velocity.

01:26 Now for part b, the acceleration of the monkey is not zero.

01:32 So for part b we have the sum of forces in the wide direction equaling the mass times the acceleration of the wide direction here this was zero here we can't say that we can actually only say that 2 t minus m g equals then the mass times the acceleration in the wide direction and should stay constant and so the tension t would be equaling to the mass multiplied by the acceleration plus the acceleration due to gravity, but again, divided by two.

02:07 And so this would be equal to the combined mass of the monkey and the plate, 100 .0 kilograms.

02:14 This would then be multiplied by 2 .45 plus 9 .81 meters per second squared...

Please give Ace some feedback