A 2.0 kg steel block is at rest on a steel table. A...

Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces that are in contact. It has a maximum value determined by the normal force and the coefficient of static friction, and any applied force must overcome this maximum value to set an object in motion.

Kinetic Friction

Kinetic friction is the force that opposes the motion of an object already sliding over a surface. It is usually less than the maximum static friction and is calculated using the coefficient of kinetic friction multiplied by the normal force, playing a key role in determining the net force and resulting acceleration once the object begins to move.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m*a). This principle is essential for relating the forces acting on an object, such as tension and friction, to its acceleration and subsequent motion.

Work-Energy Principle

The work-energy principle connects the work done by all the forces acting on an object to its change in kinetic energy. It is particularly useful in problems where an object’s speed is determined after moving a certain distance under constant forces, allowing the calculation of the final velocity by equating the net work with the kinetic energy gained.

Kinematics

Kinematics involves the study of motion without considering its causes. It includes the equations of motion that relate displacement, velocity, acceleration, and time. These equations are used to calculate the final speed or displacement of an object when its acceleration and initial conditions are known.

Transcript

00:01 In this question, we're told a 2 -kilogram steel block rests on a steel table, and we're told that a string pulls on the block.

00:09 We're asked to calculate a number of things, the first of which is what is the minimum string tension needed to move the block.

00:19 So first of all, this question is going to involve a lot of calculations with friction.

00:26 And you might have noticed that no coefficients of friction are given in the problem.

00:31 This is where you'd want to refer to some sort of table that has coefficients of friction in it.

00:37 So if you look in the book in table 1 of this chapter, you will see a table with the coefficients.

00:48 And in particular, we're talking about a steel block on a steel table.

00:53 So we want to use the coefficients for steel on steel.

00:56 And so the static coefficient is 0 .8.

01:00 The kinetic coefficient is 0 .6.

01:04 So those are the values we're going to be using for our coefficients of friction.

01:10 And this is for steel on steel.

01:18 Okay, so the minimum tension needed to move the block.

01:22 If the block is not moving already, that means that we need to be focusing on static friction.

01:27 And remember that static friction can be anywhere between zero and some maximum value.

01:39 So when you're pulling on an object that's not yet moving, the static friction is going to increase, increase, increase, to match your pulling force until it can't increase anymore, which is the maximum amount of static friction.

01:53 So the minimum tension you need to use to make the block move is this equal to this static friction maximum.

02:02 So the tension that we need is, equal to the maximum static friction, which we can calculate as mu s fn.

02:12 Now for this object, there are no other horizontal or sorry, there are no other vertical forces other than the normal force and the gravitational force.

02:21 So the normal force will just be equal to m times g.

02:25 So we can solve for this tension force by summing in those numbers here.

02:30 So we've got 0 .8s.

02:34 The mass was given as 2 kilograms and then just our acceleration due to gravity.

02:43 And plugging that into the calculator, we get a value of tension of about 15 .7 newtons.

02:50 So that is the answer for part a.

02:54 Let's take a look at part b.

02:55 So in part b, we're told if the string tension is 20 neutons, what is the blocks speed after moving one meter? so instead of focusing on static, now we're talking about a kinetic situation.

03:11 Here.

03:13 And presumably on the block, we have the tension force, which is 20 newtons, pulling it forward.

03:21 And then we're going to have some amount of kinetic friction pulling backwards as well.

03:27 Now, likely these won't be balanced.

03:29 And so that will give some sort of net force and an acceleration that we can use to calculate the block speed.

03:36 So let's go ahead and calculate what this fk value will be...

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