At time t=0, block A of mass 0.225 kg and block B of mass 0.600 kg rest on a horizontal friction

At time t=0, block A of mass 0.225 kg and block B of mass...

At time $t=0,$ block $A$ of mass $0.225 \mathrm{kg}$ and block $B$ of mass $0.600 \mathrm{kg}$ rest on a horizontal frictionless surface a distance $3.40 \mathrm{m}$ apart, with block $A$ located to the left of block $B$. A horizontal force of $2.00 \mathrm{N}$ directed to the right is applied to block $A$ for a time interval $\Delta t=0.100$ s. During the same time interval, a $5.00 \mathrm{N}$ horizontal force directed to the left is applied to block $B$. How far from $B$ 's initial position do the two blocks meet? How much time has elapsed from $t=0$ until the blocks meet?

At time $t=0,$ block $A$ of mass $0.225 \mathrm{kg}$ and block $B$ of mass $0.600 \mathrm{kg}$ rest on a horizontal frictionless surface a distance $3.40 \mathrm{m}$ apart, with block $A$ located to the left of block $B$. A horizontal force of $2.00 \mathrm{N}$ directed to the
right is applied to block $A$ for a time interval $\Delta t=0.100$ s. During the same time interval, a $5.00 \mathrm{N}$ horizontal force directed to the left is applied to block $B$. How far from $B$ 's initial position do the two blocks meet? How much time has elapsed from $t=0$ until the blocks meet?

Key Concepts

Uniformly Accelerated Motion

Uniformly accelerated motion refers to motion in which the acceleration remains constant. The kinematic equations, which relate displacement, velocity, acceleration, and time, are crucial for determining how far an object travels during a period of acceleration and for predicting its subsequent motion.

Relative Motion

Relative motion involves analyzing the movement of two or more objects with respect to each other. By considering the relative speeds and positions of the blocks, one can determine the time and location at which they meet.

Impulse and Momentum

Impulse is the product of the force applied and the time interval during which it acts, and it results in a change in an object’s momentum. This concept allows us to determine the speed attained by an object after a force is applied for a short interval, regardless of the complexities of the force application.

Newton’s Second Law

Newton’s Second Law states that the net force acting on an object is equal to its mass times its acceleration. This fundamental principle is used to compute the acceleration during periods of constant force and plays a key role in predicting the motion of each block.

Transcript

00:01 Okay, so in this problem we're going to use newton's role and kinetic of particle to solve this problem.

00:12 Okay, so first thing we need to know is that when the two newton of force applied to block a, okay? there will be an acceleration, we call it its acceleration south of a, equal.

00:35 4 we know it equal to f .a.

00:42 Divided by n .a.

00:45 By plugging the number, we have 2 newton.

00:52 The mass of block a is 0 .225, okay, kilogram.

01:11 Okay, so which gives a acceleration of 8 .89 meter per second.

01:31 So the same for b we have fb divided by n b equal this is 5 nton and this is 0 .6 kilogram okay so which get us a acceleration of 8 .3 meter per second square.

02:19 So that's the first step.

02:22 So the next step is to calculate the displacement during the time when the force is applied on these two blocks.

02:42 Okay, so by calculate the displacement, we use the equation of s .a.

02:52 Equal to 1 half, okay, delta t squared.

03:04 Because the initial velocity, in this case, for both blocks, is zero.

03:12 So we can use this equation like this.

03:14 Okay, by plugging the number, we have one half.

03:20 This is a point a nine.

03:25 The delta t equal to 0 .1 second.

03:29 So 0 .1 square.

03:35 Okay.

03:36 So in this case it gets get 0 .04 meter.