Answer:
F₃ = 122.88 N
θ₃ = 20.63°
Explanation:
First we find the components of F₁:
For x-component:
F₁ₓ = F₁ Cos θ₁
F₁ₓ = (50 N) Cos 60°
F₁ₓ = 25 N
For y-component:
F₁y = F₁ Sin θ₁
F₁y = (50 N) Sin 60°
F₁y = 43.3 N
Now, for F₂. As, F₂ acts along x-axis. Therefore, its y-component will be zero and its x-xomponent will be equal to the magnitude of force itself:
F₂ₓ = F₂ = 90 N
F₂y = 0 N
Now, for the resultant force on ball to be zero, the sum of x-components of the forces and the sum of the y-component of the forces must also be equal to zero:
F₁ₓ + F₂ₓ + F₃ₓ = 0 N
25 N + 90 N + F₃ₓ = 0 N
F₃ₓ = - 115 N
for y-components:
F₁y + F₂y + F₃y = 0 N
43.3 N + 0 N + F₃y = 0 N
F₃y = - 43.3 N
Now, the magnitude of F₃ can be found as:
F₃ = √F₃ₓ² + F₃y²
F₃ = √[(- 115 N)² + (- 43.3 N)²]
<u>F₃ = 122.88 N</u>
and the direction is given as:
θ₃ = tan⁻¹(F₃y/F₃ₓ) = tan⁻¹(-43.3 N/-115 N)
<u>θ₃ = 20.63°</u>
We can solve the problem by applying Newton's second law, which states that the resultant of the forces acting on an object is equal to the product between its mass and its acceleration:
We should consider two different directions: the direction perpendicular to the inclined plane and the direction parallel to it. Let's write the equations of the forces along the two directions, decomposing the weight of the object (mg):
(parallel direction) (1)
(perpendicular direction) (2)
where
is the angle of the inclined plane, N is the normal reaction of the plane,
is the frictional force, with
being the coefficient of friction.
From eq.(2), we find
and if we substitute into eq.(1), we can find the acceleration of the block:
from which
Answer:
The appearance and composition of meteorites is what we would expect if metal and rock condensed and increased as our theory suggests.
Explanation:
The planets and most of their satellites were formed by accretion of matter that accumulated around the largest pieces of the proto-nebula. After a chaotic succession of collisions, mergers and reconstruction processes, they acquired a size similar to the current one and moved until they were in the positions we know.
The area closest to the Sun was too warm to retain light materials. That is why the inner planets are small and rocky, while the outer ones are large and gaseous. The evolution of the Solar System has not stopped, but, after the initial chaos, most of the materials are now part of bodies located in more or less stable orbits.
Any theory that attempts to explain the formation of the Solar System should take into account that the Sun rotates slowly and only has 1 percent of the angular momentum, but it has 99.9% of its mass, while the planets have 99% of the angular momentum and only 0.1% of the mass. One of the explanations argues that, at first, the Sun was much colder; The density of its materials was slowing its rotation, while warming, until a certain balance was achieved.
