Vf = 0 + 3.5•8.7
= 30.45 m/s
<h3>Question -:</h3>
The Earth orbits around the sun because the gravitational force that the sun
exerts on the Earth:
O A. causes Earth's acceleration toward the sun.
O B. is very small because the sun is so far from the Earth.
O c. is smaller than the force the Earth exerts on the sun.
O D. pushes the Earth away from the sun.
<h3>Answer -:</h3>
O A. causes Earth's acceleration toward the sun.
<em>I </em><em>hope </em><em>this</em><em> </em><em>helps</em><em>,</em><em> </em><em>have </em><em>a </em><em>nice </em><em>time </em><em>ahead!</em>
Answer:
39.81 N
Explanation:
I attached an image of the free body diagrams I drew of crate #1 and #2.
Using these diagram, we can set up a system of equations for the sum of forces in the x and y direction.
∑Fₓ = maₓ
∑Fᵧ = maᵧ
Let's start with the free body diagram for crate #2. Let's set the positive direction on top and the negative direction on the bottom. We can see that the forces acting on crate #2 are in the y-direction, so let's use Newton's 2nd Law to write this equation:
- ∑Fᵧ = maᵧ
- T₁ - m₂g = m₂aᵧ
Note that the tension and acceleration are constant throughout the system since the string has a negligible mass. Therefore, we don't really need to write the subscripts under T and a, but I am doing so just so there is no confusion.
Let's solve for T in the equation...
- T₁ = m₂aᵧ + m₂g
- T₁ = m₂(a + g)
We'll come back to this equation later. Now let's go to the free body diagram for crate #1.
We want to solve for the forces in the x-direction now. Let's set the leftwards direction to be positive and the rightwards direction to be negative.
The normal force is equal to the x-component of the force of gravity.
- (F_n · μ_k) - m₁g sinΘ = m₁aₓ
- (F_g cosΘ · μ_k) - m₁g sinΘ = m₁aₓ
- [m₁g cos(30) · 0.28] - [m₁g sin(30)] = m₁aₓ
- [(6)(9.8)cos(30) · 0.28] - [(6)(9.8)sin(30)] = (6)aₓ
- [2.539595871] - [-58.0962595] = 6aₓ
- 60.63585537 = 6aₓ
- aₓ = 10.1059759 m/s²
Now let's go back to this equation:
We have 3 known variables and we can solve for the tension force.
- T = 2(10.1059759 + 9.8)
- T = 2(19.9059759)
- T = 39.8119518 N
The tension force is the same throughout the string, therefore, the tension in the string connecting M2 and M3 is 39.81 N.
Answer:
D. Wind turbines take up a lot of space.
Explanation:
In wind turbines the kinetic energy received by the air molecules is converted into electrical energy by the use of turbines
So here in order to get more kinetic energy from air we need more crossectional area of the wind mill to interact with the air
So here we need the large size of turbines
so this is the main disadvantage of the wind turbines because it needs large area to install the whole setup also the efficiency of this turbine is small so it needs large number of wind mills to setup good output power
so correct answer will be
D. Wind turbines take up a lot of space.
Correct question is;
A ballet dancer spins with 2.4 rev/s with her arms outstretched,when the moment of inertia about axis of rotation is I. With her arms folded,the moment of inertia about the same axis becomes 0.6I about the same axis. Calculate the new rate of spin.
Answer:
4 rev/s
Explanation:
We are given;
Initial Angular velocity; ω_i = 2.4 rev/s
Initial moment of inertia; I_i = I
Final moment of inertia; I_f = 0.6I
From conservation of angular momentum, we have;
I_i × ω_i = I_f × ω_f
Where ω_f is the new rate of spin.
Thus, let's make it the subject to get;
ω_f = (I_i × ω_i/I_f)
Plugging in relevant values, we have;
ω_f = (I × 2.4/0.6I)
I will cancel out to give;
ω_f = 2.4/0.6
ω_f = 4 rev/s