three forces acting on an object are given by f1 195i 715j n f2 455i 115j n and f3 43i n the obj

Name: three forces acting on an object are given by f1 195i 715j n f2 455i 115j n and f3 43i n the object experiences an acceleration of magnitude 390 ms2 a what is the direction of the accelerati 29364
Uploaded: 2022-05-09T08:01:59-08:00
Duration: 5 min 19 s
Channel: Madhur L
Description: three forces acting on an object are given by f1 195i 715j n f2 455i 115j n and f3 43i n the object experiences an acceleration of magnitude 390 ms2 a what is the direction of the accelerati 29364

To solve the problem step by step, we will analyze the forces acting on the object, calculate th

Three forces acting on an object are given by f1 195i 715j n...

Three forces acting on an object are given by F1 = (−1.95î + 7.15ĵ) N, F2 = (4.55î − 1.15ĵ) N, and F3 = (−43î) N. The object experiences an acceleration of magnitude 3.90 m/s2. (a) What is the direction of the acceleration? ° (counterclockwise from the +x-axis) (b) What is the mass of the object? kg (c) If the object is initially at rest, what is its speed after 20.0 s? m/s (d) What are the velocity components of the object after 20.0 s? (Let the velocity be denoted by v. ) v = î + ĵ m/s

Transcript

0:00 Hello students.

00:01 So to solve this question, let us first find the x component of force f, which will be given as fx equals f1x plus f2x plus f3x.

00:22 Now putting the values here, we get the x component of f, that is fx equals minus 1 .75 plus 5 .40 minus 5 .40, 49 now this will give us minus 45 .35 newton similarly the y component of force f is given as fy equals f1y plus f2y plus f3y again putting the values here we get the y component that is f y equals 6 .00 minus 2 .40 plus 0 which will give us 3 .60 newton.

01:17 Now that we have calculated x and y components, let us find the first part a, that is direction of acceleration.

01:26 So using the formula, theta equals tan inverse f y divided by f x here the angle is plus 180 degree now using this formula let us find the direction of acceleration putting the values here we get theta equals tan inverse f y is 3 .60 divided by minus 45 .35 plus 180 degree.

01:58 Now, the final answer for part a, theta, is 175 .5 degrees.

02:07 So for b part, we need to find the mass of the object.

02:11 For that, let us find the magnitude of force first, which will be minus 45 .355 square plus 3 .6 .6.

02:23 Square under root.

02:26 This will give us the result of 45 .49 newton's.

02:32 Now, mass of the object can be calculated using m equals f divided by acceleration a.

02:40 Putting the value here we get 45 .49 divided by acceleration is 3 .80.

02:50 This will give us the result 11 .97...