(II) The two forces 𝐅⃗1 and 𝐅⃗2 shown in Fig, 40 a and b (looking down) act on a 18.5 -kg object

step 1 So for a part A, let's just draw a diagram. So here would be F sub 1. This would be our angle th

(II) The two forces 𝐅⃗1 and 𝐅⃗2 shown in Fig, 40 a and b...

(II) The two forces $\vec{\mathbf{F}}_{1}$ and $\vec{\mathbf{F}}_{2}$ shown in Fig, 40 $\mathrm{a}$ and $\mathrm{b}$ (looking down) act on a 18.5 -kg object on a frictionless tabletop. If $F_{1}=10.2 \mathrm{N}$ and $F_{2}=16.0 \mathrm{N},$ find the net force on the object and its acceleration for (a) and (b).

(II) The two forces $\vec{\mathbf{F}}_{1}$ and $\vec{\mathbf{F}}_{2}$ shown in Fig, 40 $\mathrm{a}$ and $\mathrm{b}$ (looking
down) act on a 18.5 -kg object on a frictionless tabletop. If $F_{1}=10.2 \mathrm{N}$ and $F_{2}=16.0 \mathrm{N},$ find the net force on the
object and its acceleration for (a) and (b).

Key Concepts

Newton's Second Law

This principle states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = m * a). It is fundamental in linking the forces acting on an object to the resulting motion, and it is used to calculate acceleration once the net force is known.

Vector Addition

Since force is a vector quantity, combining multiple forces requires vector addition. This involves taking into account both the magnitude and direction of each force, and using methods such as graphical addition or breaking forces into components to find the resultant or net force.

Vector Components

For forces applied at different angles, breaking each force into its orthogonal components (typically horizontal and vertical) simplifies the process of vector addition. Once decomposed, the components can be added algebraically to determine the net force in each direction before recombining to find the overall resultant.

Frictionless Motion

The concept of a frictionless surface implies there is no resistive force opposing the motion of the object. This simplifies the analysis because the net applied force is not reduced by friction and directly causes acceleration according to Newton's second law.

Transcript

00:01 So for a part a, let's just draw a diagram.

00:09 So here would be f sub 1.

00:12 This would be our angle theta.

00:15 Here would be f sub 2.

00:22 And then this right here, this vector right here, would simply be our net force.

00:30 So we can say that for part, for part a, rather, the force net in the x direction would be equal to negative force.

00:43 Of 1 it is going to the left so we'll say it's negative and this will be negative 10 .2 newtons and then force net sub y this would be equal to negative force sub 2 and this is equaling negative 16 .0 newtons now in order to find the magnitude of the force net this would be equal to the square root of the sum of the squares so negative 10 .2 squared plus negative 16 .0 squared all to the one half power and we find that the magnitude of the net force is going to be 19 .0 newtons now let's find a direction so here we can say that's the direction theta would be arc tan of the y component negative 16 .0 divided by the x component negative 10 .2 this is going to equal 57 .5 degrees and this would be 57 .5 degrees below negative x axis so we can say that the acceleration would then be equal to the net force divided by the mass so this would be 19 .0 newtons divided by the mass of 18 .5 kilograms and we have an acceleration of 1 .03 meters per second squared.

02:34 Again, 57 .5 degrees below the negative x -axis.

02:39 Now, for part b, let's draw again, quick diagram.

02:46 This would be our x -axis.

02:48 This would be our y -axis.

02:50 And here would be our force of one.

02:54 This would be a 30 -degree angle.

02:57 This would be our force net.

03:02 This would be our angle theta.

03:06 And then going straight up, let's actually extend this, going straight up would be our force sub 2...