Chapter 5: Q 74P (page 122)

The only two forces acting on a body have magnitudes of $20 N$ and $35 N$ and directions that differ by $80^{\circ}$ . The resulting acceleration has a magnitude of role="math" localid="1655525874259" $20 m / s^{2}$ . What is the mass of the body?

Short Answer

Expert verified

Mass of the body is $m = 2.6 k g .$

Step by step solution

Given information

It is given that,

$F_{1} = 20 N F_{2} = 35 N$

The angle between $F_{1}$ and $F_{2}$ is $θ = 80^{\circ}$

Determining the concept

The problem is based on Newton’s second law of motion which states that the rate of change of momentum of a body is equal in both magnitude and direction of the force acting on it.Also this involves resolution of vectors.

Formula:

According to the Newton’s second law of motion,

$F_{n e t} = \sum_{}^{} M a (i)$

Determining the mass of the body

Free Body Diagram:

$\vec{F_{1}} = 20 \hat{i} \vec{F_{2}} = 35 \cos (80) \hat{i} + 35 \sin (80) \hat{j} \vec{F_{2}} = 6.1 \hat{i} + 34.5 \hat{j}$

Now resultant force will be:

role="math" localid="1655527433958" $\vec{F} = \vec{F_{1}} + \vec{F_{2}} \vec{F} = (20 + 6.1) \hat{i} + 34.5 \hat{j} \vec{F} = 26.1 \hat{i} + 34.5 \hat{j}$

Magnitude of resultant is,

$|\overset{⇀}{F}| = \sqrt{{(26.1)}^{2} + {(34.5)}^{2}} = 43.3 N$

Thus, using equation (i),

$43.3 = m \times 20 m = 2.16 k g$

Hence, the mass of the body is $m = 2.16 k g$

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The only two forces acting on a body have magnitudes of $20 N$ and $35 N$ and directions that differ by $80^{\circ}$ . The resulting acceleration has a magnitude of role="math" localid="1655525874259" $20 m / s^{2}$ . What is the mass of the body?

Short Answer

Step by step solution

Given information

Determining the concept

Determining the mass of the body

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The only two forces acting on a body have magnitudes of 20Nand 35Nand directions that differ by 80∘. The resulting acceleration has a magnitude of role="math" localid="1655525874259" 20m/s2. What is the mass of the body?

Short Answer

Step by step solution

Given information

Determining the concept

Determining the mass of the body

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Measurements

Magnetism and Electromagnetic Induction

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Study anywhere. Anytime. Across all devices.

The only two forces acting on a body have magnitudes of $20 N$ and $35 N$ and directions that differ by $80^{\circ}$ . The resulting acceleration has a magnitude of role="math" localid="1655525874259" $20 m / s^{2}$ . What is the mass of the body?