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>
The original kinetic energy will be 0 J and the final kinetic energy will be 7500 J and the amount of work utilized will be similar to the final kinetic energy i.e., 7500 J.
<u>Explanation:</u>
As it is known that the kinetic energy is defined as the energy exhibited by the moving objects. So the kinetic energy is equal to the product of mass and square of the velocity attained by the car. Thus,

So the initial kinetic energy will be the energy exerted by the car at the initial state when the initial velocity is zero. Thus the initial kinetic energy will be zero.
The final kinetic energy is
= 7500 J
As the work done is the energy required to start the car from zero velocity to 5 m/s velocity.
Work done = Final Kinetic energy - Initial Kinetic energy
Thus the work utilized for moving the car is
Work done = 7500 J - 0 J = 7500 J
Thus, the initial kinetic energy of the car is zero, the final kinetic energy is 7500 J and the work utilized by the car is also 7500 J.
I think that mechanism is called a <em>"lens turret"</em>.
Answer:
Drilling into the seafloor off Mexico, scientists have extracted a unique geologic record of the single worst day in the history of life on Earth, when a city-sized asteroid smashed into the planet 65 million years ago, wiping out the dinosaurs and three-quarters of all other life.
Their analysis of these new rock samples from the Chicxulub crater, made public Monday, reveals a parfait of debris deposited in layers almost minute-by-minute at the heart of the impact during the first day of a global catastrophe. It records traces of the explosive melting, massive earthquakes, tsunamis, landslides and wildfires as the immense asteroid blasted a hole 100 miles wide and 12 miles deep, the scientists said.
The new period is D) √2 T

<h3>Further explanation</h3>
Let's recall Elastic Potential Energy and Period of Simple Pendulum formula as follows:

where:
<em>Ep = elastic potential energy ( J )</em>
<em>k = spring constant ( N/m )</em>
<em>x = spring extension ( compression ) ( m )</em>


where:
<em>T = period of simple pendulum ( s )</em>
<em>L = length of pendulum ( m )</em>
<em>g = gravitational acceleration ( m/s² )</em>
Let us now tackle the problem!

<u>Given:</u>
initial length of pendulum = L₁ = L
initial mass = M₁ = M
final length of pendulum = L₂ = 2L
final mass = M₂ = 2M
initial period = T₁ = T
<u>Asked:</u>
final period = T₂ = ?
<u>Solution:</u>






<h3>Learn more</h3>

<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Elasticity