ssm Two forces 𝐅A and 𝐅B are applied to an object whose mass is 8.0 kg . The larger force is 𝐅A

Ssm Two forces 𝐅A and 𝐅B are applied to an object whose mass...

ssm Two forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ are applied to an object whose mass is 8.0 $\mathrm{kg}$ . The larger force is $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ . When both forces point due east, the object's acceleration has a magnitude of 0.50 $\mathrm{m} / \mathrm{s}^{2}$ . However, when $\overline{\mathrm{F}}_{\mathrm{A}}$ points due east and $\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ points due west, the acceleration is 0.40 $\mathrm{m} / \mathrm{s}^{2}$ due east. Find (a) the magnitude of $\overrightarrow{\mathbf{F}}_{\mathbf{A}}$ and $\quad(\mathbf{b})$ the magnitude of $\overrightarrow{\mathbf{F}}_{\mathbf{B}}$.

Key Concepts

Newton's Second Law

Newton's Second Law of motion asserts that the net force acting on an object is equal to the product of its mass and its acceleration. This foundational principle provides a direct relationship between the forces acting on an object and the resulting change in its motion, enabling the analysis of various dynamic systems by relating known quantities such as mass and acceleration to the unknown forces.

Vector Addition of Forces

Because forces have both magnitude and direction, they must be treated as vectors. The principle of vector addition allows multiple forces to be combined by summing their components along each axis. This approach is critical in physics problems where forces may act in opposite or various directions, as it determines the net force that governs the object's acceleration.

Net Force in Opposing Directions

When forces act in opposing directions, their effects subtract from one another, resulting in a net force that is less than the sum of their magnitudes. This concept is essential for understanding how simultaneous but opposite forces influence the overall acceleration of an object and is crucial in solving problems where the forces change their relative directions.

Transcript

00:01 To begin this question, we can apply newton's second law in both situations.

00:05 So, for the first situation, newton's second law tells us that the net force is equal to the object's mass times the acceleration.

00:15 But the object's net force, in this case, is equal to f a plus fb.

00:22 He knows that i'm adopting that everyone pointing towards the right is positive and everyone pointing towards the left is negative.

00:30 So here we have f .a plus fb, and this is equal to the mass times the acceleration.

00:39 On the second situation, the net force, let me do this.

00:44 In the second situation, the net force is equal again to the mass times the acceleration.

00:50 But now the acceleration is different, so let me call it a prime.

00:54 And the net force is given by f a minus fb, because now the force b is point.

01:02 To the left.

01:04 And this is equal to the mass times the new acceleration.

01:08 So this is what you get by using newton's second law.

01:12 Now what can we do to solve for f .a and fb? well, note that this is a system of equations.

01:19 In the first situation, we have f .a plus fb equals to 8 times 0 .5, and this is equals to 4.

01:32 Therefore, in the first situation, we have f .a plus fb is equal to 4.

01:40 In the second situation, we have f .a.

01:45 Minus fb is equal to 0 .4 times 8, which is equal to 3 .2...

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