An object is acted upon by the forces 𝐅1=⟨10,6,3⟩and 𝐅2=⟨0,4,9⟩. Find the force 𝐅3 that must act

Name: Problem 56, Chapter 11: Calculus Early Transcendentals
Uploaded: 2022-01-31T14:57:01-08:00
Duration: 1 min 3 s
Channel: Carson Merrill
Description: An object is acted upon by the forces 𝐅1=⟨10,6,3⟩and 𝐅2=⟨0,4,9⟩. Find the force 𝐅3 that must act on the object so that the sum of the forces is zero.

step 1 So here we're looking at a physics example in which we have an object acted upon by three forces

Question

An object is acted upon by the forces $\mathbf{F}_{1}=\langle 10,6,3\rangle$ and $\mathbf{F}_{2}=\langle 0,4,9\rangle .$ Find the force $\mathbf{F}_{3}$ that must act on the object so that the sum of the forces is zero.

   An object is acted upon by the forces $\mathbf{F}_{1}=\langle 10,6,3\rangle$ and $\mathbf{F}_{2}=\langle 0,4,9\rangle .$ Find the force $\mathbf{F}_{3}$ that must act on the object so that the sum of the forces is zero.

Calculus Early Transcendentals

William Briggs, Lyle… 2nd Edition

Chapter 11, Problem 56

Instant Answer

Solved by Expert Carson Merrill

01/31/2022

Step 1

We do this by adding their corresponding components: $$\mathbf{F}_{1} + \mathbf{F}_{2} = \langle 10,6,3\rangle + \langle 0,4,9\rangle = \langle 10+0,6+4,3+9\rangle = \langle 10,10,12\rangle$$ Show more…

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An object is acted upon by the forces $\mathbf{F}_{1}=\langle 10,6,3\rangle$ and $\mathbf{F}_{2}=\langle 0,4,9\rangle .$ Find the force $\mathbf{F}_{3}$ that must act on the object so that the sum of the forces is zero.

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Key Concepts

Vector Addition

Vector addition involves combining two or more vectors by adding their corresponding components. This process is fundamental when working with forces, as it allows for the determination of a resultant vector that represents the combined effect of all individual forces acting on an object.

Equilibrium

Equilibrium occurs when the net force acting on an object is zero, meaning that all the forces cancel out. This concept is crucial in both static and dynamic contexts, as it helps in analyzing situations where an object remains at rest or moves with constant velocity.

Inverse (Negative) Vector

An inverse or negative vector is one that has the same magnitude but the opposite direction to the original vector. This concept is used to counteract a given vector, and when added to it, the resultant is a zero vector, which is essential for achieving equilibrium.

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