Repeat Problem 83 , but now with the block accelerated up a frictionless plane inclined at 5.0^∘

Repeat Problem 83 , but now with the block accelerated up a...

Key Concepts

Newton's Laws of Motion

This concept refers to the fundamental principles that govern how forces affect the motion of objects. In the context of accelerated motion, Newton’s second law (F = ma) is crucial for relating the net forces acting on an object to its acceleration, especially when analyzing forces on an inclined plane.

Decomposition of Forces

In many physics problems, particularly those involving inclined planes, it is important to break down the forces acting on an object into components that are parallel and perpendicular to the plane. This allows for a more straightforward analysis of the net force responsible for accelerating the object along the plane.

Inclined Plane Dynamics

The study of motion on an inclined plane involves analyzing how the gravitational force is distributed along the plane. This concept is essential for understanding how the angle of the incline influences both the component of gravity that causes acceleration and the normal force that acts perpendicular to the surface.

Frictionless Motion

When a surface is frictionless, there is no resistive force opposing the motion of an object. This simplifies the problem by ensuring that only factors such as gravitational components and any externally applied forces need to be considered in the analysis of the object's acceleration.

Transcript

00:01 In this cushion, it is given that a uniform meter stick is suspended from the ceiling through two vertical strings of equal length and a small object of mass 20 gram is placed on the stick at a distance of 70 semi from the left end.

00:16 Now we have to find the tensions in the two strings.

00:19 So first of all i am drawing the diagram for this given tuition.

00:25 So let is this is the ceiling and these are the two strings.

00:32 Through which the meter streak is connected this is our meter streak now we have given that a small object is placed at a distance of 70 semi let this this distance is given to us which is 70 semi now i am showing the all the forces acting on this system first the weight of this meter stick that is acting at the center of this metric stick that is let m1 into g and this is m2 into g which is the weight of this block let the tension in this string is t1 and tension in this streak is t2 and so am writing here all the given data that is mass of the metastricht that is m1 is 200 gram mass of the block that is m2 is equal to 20 and length of the string that is l is given to us which is 1 meter now we know that as the system is in equilibrium so the net torque about o will be 0 so net torque is 0 about this point that is o so writing the net torque so torque due to this tension is t1 into r1 which is into anti -clockwise direction and torque due to this tension force is minus t2 into r2 because this is into clockwise direction and torque due to this is 0 and torque due to this weight is minus m1g into r3 r1r2 and r3 are the distances of this forces from this point that is o so is 0 .7 meter, r2 is 0 .3 meter and r3 is 0 .2 meter.

03:04 Now put all the data in this equation.

03:07 So from here we get t1 into 0 .7 minus t2 into 0 .3 minus mass is given to us that is 2 into 0 .2 into g...

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