thebestoddly
Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Two men pull on a 31-kg box with forces 8.3 N and 6.6 N in opposite directions.
Find the resultant acceleration of the box and the direction in which the box moves.

Please HURRY

Sagot :

VirαtKσhli

Answer:

0.054m/s²

Explanation:

Here we are given that a 31kg block is being pulled by two men who apply forces of 8.3N and 6.6N in opposite directions .

So we know that ,

[tex]\sf \longrightarrow \boxed{\red{\rm F_{net}= \sqrt{F_1^2+F_2^2+2F_1F_2cos\theta }}}[/tex]

where [tex]\theta[/tex] is the angle between the forces .

  • Since the forces act in opposite directions , the angle between them will be 180° .

[tex]\sf \longrightarrow F_{net}= \sqrt{ (8.3N)^2+(6.6N)^2+2(8.3)(6.6)(cos180^o)}\\ [/tex]

  • Value of cos 180° = -1

[tex]\sf \longrightarrow F_{net}= \sqrt{ (8.3N)^2+(6.6N)^2+2(8.3)(6.6)(-1)}\\ [/tex]

[tex]\sf \longrightarrow F_{net}= \sqrt{ (8.3N)^2+(6.6N)^2-2(8.3)(6.6)}\\ [/tex]

  • RHS is in form of (a-b)² = a² + b² -2ab inside the square root .

[tex]\sf \longrightarrow F_{net}=\sqrt{( 8.3N - 6.6N)^2} \\ [/tex]

[tex]\sf \longrightarrow F_{net}= 8.3N - 6.6N \\ [/tex]

[tex]\sf \longrightarrow \red{ F_{net}= 1.7N} \\ [/tex]

Now we know that ,

[tex]\sf \longrightarrow F_{net}= mass * acceleration \\ [/tex]

[tex]\sf \longrightarrow 1.7N = 31kg * a\\ [/tex]

[tex]\sf \longrightarrow a =\dfrac{1.7N}{31kg}\\ [/tex]

[tex]\sf \longrightarrow \underline{\boxed{\bf accl^n = 0.054 m/s^2}} \\ [/tex]

  • And the box will move in the direction of application of 8.3N force .
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.