a body is under the action of two force 7 newton and 10 Newton. find the 2 Force if (a) the force parrallel and the act in the same direction (b) the force are parallel and actin opposite direction (c) the 2 force and inclined in at angle of 60° to each other (d) the 2 force are inclined at angle of 160° (e) the two forces are at 90° to each order?

Phenominalpsam24

2 years ago

When two forces are parallel and act in the same direction:
Resultant force = √(7^2 + 10^2) = √(49 + 100) = √149 ≈ 12.21 Newtons

(b) When two forces are parallel and act in opposite directions:
Resultant force = |7 - 10| = 3 Newtons

(c) When the two forces are inclined at an angle of 60° to each other:
Resultant force = √(7^2 + 10^2 + 2 * 7 * 10 * cos(60°)) = √(49 + 100 + 70) = √219 ≈ 14.8 Newtons

(d) When the two forces are inclined at an angle of 160°:
Resultant force = √(7^2 + 10^2 - 2 * 7 * 10 * cos(160°)) = √(49 + 100 + 140) = √289 ≈ 17 Newtons

(e) When the two forces are at 90° to each other:
Resultant force = √(7^2 + 10^2) = √(49 + 100) = √149 ≈ 12.21 Newtons

These are the magnitudes of the resultant forces for each of the given scenarios.

All_for_one

2 years ago

To find the resultant of two forces, you can use vector addition. The magnitude of the resultant force can be calculated using the Pythagorean theorem, and the direction can be found using trigonometry.

Let's calculate the results for each scenario:

(a) When the forces are parallel and act in the same direction:

F1 = 7 N
F2 = 10 N

Resultant force (R) = F1 + F2
R = 7 N + 10 N
R = 17 N

(b) When the forces are parallel and act in opposite directions:

F1 = 7 N
F2 = 10 N

Resultant force (R) = |F1 - F2| (taking the absolute value)
R = |7 N - 10 N|
R = |-3 N| = 3 N

(c) When the two forces are inclined at an angle of 60° to each other:

F1 = 7 N
F2 = 10 N
θ = 60°

Resultant force (R) can be calculated as:

R = √(F1² + F2² + 2 * F1 * F2 * cos(θ))

R = √((7 N)² + (10 N)² + 2 * 7 N * 10 N * cos(60°))
R = √(49 N² + 100 N² + 140 N² * 0.5)
R = √(49 N² + 100 N² + 70 N²)
R = √(219 N²)
R ≈ 14.8 N

(d) When the two forces are inclined at an angle of 160° (180° - 160°):

F1 = 7 N
F2 = 10 N
θ = 160°

Use the same formula as in (c) with θ = 160°:

R = √(F1² + F2² + 2 * F1 * F2 * cos(θ))

R = √((7 N)² + (10 N)² + 2 * 7 N * 10 N * cos(160°))
R = √(49 N² + 100 N² - 140 N² * 0.5)
R = √(49 N² + 100 N² - 70 N²)
R = √(79 N²)
R ≈ 8.9 N

(e) When the two forces are at 90° to each other:

F1 = 7 N
F2 = 10 N
θ = 90°

Resultant force (R) can be calculated using the Pythagorean theorem:

R = √(F1² + F2²)
R = √((7 N)² + (10 N)²)
R = √(49 N² + 100 N²)
R = √(149 N²)
R ≈ 12.2 N

So, for each scenario:

(a) R = 17 N
(b) R = 3 N
(c) R ≈ 14.8 N
(d) R ≈ 8.9 N
(e) R ≈ 12.2 N