A force vec F =F x hat i +F y hat j acts on a particle that undergoes a displacement of vec s =s x hat i +s y hat j where F x =7 N , F y =-3 N , s x =4 m , and s y =1 m . Find the work done by the force on the particle . Answer in units of J.

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\large {\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

[tex]\overrightarrow{F} = 7 \widehat{i} - 3 \widehat{j}[/tex]

[tex]\overrightarrow{s} = 4 \widehat{i} + 1 \widehat{j}[/tex]

Unknown:

W = ?

Solution:

[tex]W = \overrightarrow{F} \cdot \overrightarrow{s}[/tex]

[tex]W = (7 \widehat{i} - 3 \widehat{j}) \cdot (4 \widehat{i} + 1 \widehat{j})[/tex]

[tex]W = 7(4) - 3(1)[/tex]

[tex]W = 28 - 3[/tex]

[tex]W = 25 \texttt{ Joule}[/tex]

[tex]\texttt{ }[/tex]

Conclusion:

The work done by the force on the particle is 25 Joule

[tex]\texttt{ }[/tex]

Learn more

Impacts of Gravity : https://brainly.com/question/5330244
Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
The Acceleration Due To Gravity : https://brainly.com/question/4189441
Newton's Law of Motion: https://brainly.com/question/10431582
Example of Newton's Law: https://brainly.com/question/498822

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

#LearnwithBrainly