The 50-kg block A is released from rest. Determine the velocity of the 15 -kg block B in 2 s.

Name: Problem 22, Chapter 13: Engineering Mechanics: Statics and Dynamics
Uploaded: 2020-09-29T22:10:41-08:00
Duration: 9 min 39 s
Channel: Guilherme Barros
Description: The 50-kg block A is released from rest. Determine the velocity of the 15 -kg block B in 2 s.

The 50-kg block A is released from rest. Determine the...

Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). This fundamental principle is used to relate the forces acting on an object to its resulting acceleration and is essential in dynamics problems involving multiple objects or forces.

Uniformly Accelerated Motion

The kinematic equations for uniformly accelerated motion allow the calculation of an object's velocity, displacement, and time when the acceleration is constant. These equations, such as v = u + at, are used to predict the motion of objects starting from rest or with an initial velocity under constant acceleration.

Free-Body Diagrams

Free-body diagrams are visual tools used to represent all the forces acting on an individual object. By isolating each object and illustrating the forces, one can systematically apply Newton’s laws to analyze the dynamics of the system and determine unknown forces or accelerations.

Constraint Relationships in Connected Systems

In systems where objects are connected, such as by ropes or pulleys, the motion of one object is not independent of the other. Constraint relationships help to relate the accelerations and velocities of the connected objects, ensuring that the interdependence imposed by the connection is properly taken into account.

Transcript

00:01 In this exercise, we have a system of pulleys as shown here in the picture.

00:06 We have block a that has a mass of 50 kilograms, and block b that has a mass of 15 kilograms.

00:18 And the string represented in blue here is the same string.

00:24 So the same string that connects block a to pulley e, connects pooley e to pooley d and pooley d to pooley c.

00:34 Okay.

00:36 So before actually solving the exercise, let's just make a couple of comments about how to solve problems that involve multiple pulleys.

00:49 First, we need to remember that the tension in the same string is the same, meaning that the tension propagates throughout the string.

01:07 Okay, and this, in this we assume that the string is massless and also that the pulley is massless.

01:20 And second of all, we need to consider how the height, the changing height of block b and the change in height of block a are related.

01:33 Because notice that the string length, i'm sure, string length, is constant, meaning that if block a drops by a certain height, block b will be raised by a certain height, but these two heights are not necessarily the same.

02:00 So these are two points to keep in mind when working with a system of pulleys.

02:07 So let's dive into our exercise.

02:10 Basically, we have the information that the two blocks start at rest and are going to find what is the speed of block b, okay, after a time, t that is equal to two seconds.

02:29 In order to find the speed, i'm first going to find what is the acceleration of block b, and with the acceleration, we can use the formula that the speed is equal to the initial speed, plus the acceleration times the time t.

02:51 Okay? so what do we need to do in order to find the acceleration? first of all, i'm going to apply the first principle that i wrote here.

03:04 The tension is the same throughout the string.

03:13 So basically, i'm going to draw a free body diagram for both blocks.

03:19 So let's start with point one.

03:25 Consider that we have block a here.

03:29 Notice that block a has the tension of the string pulling it upwards, and also the gravitational force pulling it down.

03:41 So we have mag.

03:47 Now newton's second law tells us that mag minus the tension t is equal to the mass of the...

04:01 The block times the acceleration of the block, which i'm calling a -a.

04:07 Okay.

04:08 This is the equation that comes from the free body diagram for block a.

04:15 Now for block b, we also have the gravitational force pulling it down...