Two forces whose magnitude are at the ratio of 3 : 5 gives resultant 35 N .If the angle of inclination is 60 degree . Find magnitude of each force ?

Question

Two forces whose magnitude are at the ratio of 3 : 5 gives resultant 35 N .If the angle of inclination is 60 degree . Find magnitude of each  force ?

Answer

Answer

Answer

To find the magnitudes of the two forces, we can use the concept of vector addition and trigonometry. Let's break down the problem step by step:

Step 1: Understanding the problem
We have two forces whose magnitudes are in a ratio of 3:5. Let's assume the magnitudes of the forces are 3x and 5x, respectively, where x is a constant.

Step 2: Finding the resultant force
The resultant force is given as 35 N. This means the vector sum of the two forces is 35 N. We can represent the forces as vectors and find their sum using the parallelogram law or triangle law of vector addition.

Step 3: Drawing a diagram
Draw a diagram representing the two forces and their resultant. Label the magnitudes of the forces (3x and 5x) and the angle of inclination (60 degrees).

Step 4: Applying trigonometry
Since we have the angle of inclination, we can use trigonometry to find the magnitudes of the forces. In this case, we can use the cosine rule.

Step 5: Applying the cosine rule
The cosine rule states that in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, the resultant force (c) is 35 N. One of the forces (a) has a magnitude of 3x, and the other force (b) has a magnitude of 5x. The angle between the two forces (C) is 60 degrees.

Applying the cosine rule, we get:

(35)^2 = (3x)^2 + (5x)^2 - 2(3x)(5x) * cos(60)

Step 6: Solving the equation
Simplifying the equation, we have:

1225 = 9x^2 + 25x^2 - 30x^2 * cos(60)

1225 = 34x^2 - 30x^2 * 0.5

1225 = 34x^2 - 15x^2

1225 = 19x^2

x^2 = 1225 / 19

x^2 ≈ 64.47

x ≈ √64.47

x ≈ 8.03

Step 7: Finding the magnitudes of the forces
Now that we have the value of x, we can substitute it back into the expressions for the magnitudes of the forces:

Magnitude of the first force = 3x ≈ 3 * 8.03 ≈ 24.1 N
Magnitude of the second force = 5x ≈ 5 * 8.03 ≈ 40.2 N

Therefore, the magnitude of the first force is approximately 24.1 N, and the magnitude of the second force is approximately 40.2 N.

In summary, we found the magnitudes of the two forces by using vector addition and trigonometry. The first force has a magnitude of approximately 24.1 N, and the second force has a magnitude of approximately 40.2 N.

Similar Class 10 Doubts

Two force whose resultant is 90N are perpendicular to each other. If one of them makes angle 60 with the resultant, calculate it's magnitude?

Two forces of magnitude 10N and 5N act at right angle to each other. The angle between the resultant and 10N force is ?

Plzz help me and clear my doubt? my question is Two forces 3N and 2N are at an angle o such that the resultant is R. The first force is now increased to 6N and the resultant become 2R.The value of is (HP PMT 2000) ch) 600?

If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is (

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company