The volume of the material that must be used to make a star with the mass of the sun is 1.2×10⁵¹ m³.
<h3>What is volume?</h3>
Volume is the amount of space occupied by an object or a plane figure.
To calculate the volume of the material that must be used to make a star with the mass of the sun, we use the formula below.
Formula:
- D = m/V............ Equation 1
Where:
- D = Density of the interstellar gas
- m = mass of the sun
- V = Volume of the material
Make V the subject of the equation
- V = m/D........... Equation 2
From the question,
Given:
- m = mass of the sun = 1.9891×10³⁰ kg
- D = 1 atom/cm³ = 1.66×10⁻²¹ kg/m³
Substitute these values into equation 2
- V = ( 1.9891×10³⁰)/(1.66×10⁻²¹)
- V = 1.2×10⁵¹ m³
Hence, The volume of the material that must be used to make a star with the mass of the sun is 1.2×10⁵¹ m³.
Learn more about volume here: brainly.com/question/1972490
Answer:
76.3 J
Explanation:
I'm assuming the distance of 4.60 m is along the incline, not the vertical distance from the bottom. I'll call this distance d, so h = d sin θ.
Initial energy = final energy
Energy in spring = gravitational energy + kinetic energy + work by friction
E = mgh + 1/2 mv² + Fd
We need to find the force of friction. To do that, draw a free body diagram.
Normal to the incline, we have the normal force pointing up and the normal component of weight (mg cos θ).
Sum of the forces in the normal direction:
∑F = ma
N - mg cos θ = 0
N = mg cos θ
Friction is defined as:
F = Nμ
Plugging in the expression for N:
F = mgμ cos θ
Substituting:
E = mgh + 1/2 mv² + (mgμ cos θ) d
E = mg (d sin θ) + 1/2 mv² + (mgμ cos θ) d
E = mgd (sin θ + μ cos θ) + 1/2 mv²
Given:
m = 1.45 kg
g = 9.90 m/s²
d = 4.60 m
θ = 29.0°
μ = 0.45
v = 5.10 m/s
Solving:
E = mgd (sin θ + μ cos θ) + 1/2 mv²
E = (1.45) (9.80) (4.60) (sin 29.0 + 0.45 cos 29.0) + 1/2 (1.45) (5.10)²
E = 76.3 J
Answer:
Explanation:
Given
Velocity = 388m/s
Height S = 2.89m
Required
Time
Using the equation of motion
S =ut+1/2gt²
2.89 = 388t+1/2(9.8)t²
2.89 = 388t+4.9t²
Rearrange
4.9t²+388t-2.89 =0
Factorize
t = -388±√388²-4(4.9)(2.89)/2(4.9)
t= -388±√(388²-56.644)/9.8
t = -388±387.93/9.8
t =0.073/9.8
t = 0.00744 seconds
Answer:
Part (a) - 1.42 rev/s
Part (b) - 5.78s
Part (c) - 6.90s
Part (d) - 33.81 rev
Explanation:
The solution to this problem requires the knowledge of constant angular acceleration motion. The equations used here are similar to those used in constant linear acceleration motion. The detailed solutio is presented in the attachment below.
