The slope of the line whose equation is 3 x

A sled is being held at rest on a slope that makes an angle theta with the horizontal. After the sled is released, it slides a d

Alenkasestr [34]

Answer:

μ = Sin θ * d₁ / (d₂ - Cos θ*d₁)

d₂ = (d₁*Sin θ) / μ

Step-by-step explanation:

a) We apply The work-energy theorem

W = ΔE

W = - Ff*d

Ff = μ*N = μ*m*g

Distance 1:

- Ff*d₁ = Ef - Ei

⇒ - (μ*m*g*Cos θ)*d₁ = (Kf+Uf) - (Ki+Ui) = (Kf+0) - (0+Ui) = Kf - Ui

Kf = 0.5*m*vf² = 0.5*m*v²

Ui = m*g*h = m*g*d₁*Sin θ

then

- (μ*m*g*Cos θ)*d₁ = 0.5*m*v² - m*g*d₁*Sin θ

⇒ - μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ (I)

Distance 2:

- Ff*d₂ = Ef - Ei

⇒ - (μ*m*g)*d₂ = (0+0) - (Ki+0) = - Ki

Ki = 0.5*m*vi² = 0.5*m*v²

then

- (μ*m*g)*d₂ = - 0.5*m*v²

⇒ μ*g*d₂ = 0.5*v² (II)

If we apply (I) + (II)

- μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ

μ*g*d₂ = 0.5*v²

⇒ μ*g (d₂ - Cos θ*d₁) = v² - g*d₁*Sin θ (III)

Applying the equation (for the distance 1) we get v:

vf² = vi² + 2*a*d = 0² + 2*(g*Sin θ)*d₁ ⇒ vf² = 2*g*Sin θ*d₁ = v²

then (from the equation III) we get

μ*g (d₂ - Cos θ*d₁) = 2*g*Sin θ*d₁ - g*d₁*Sin θ

⇒ μ (d₂ - Cos θ*d₁) = Sin θ * d₁

⇒ μ = Sin θ * d₁ / (d₂ - Cos θ*d₁)

b)

If μ is a known value

d₂ = ?

We apply The work-energy theorem again

W = ΔK ⇒ - Ff*d₂ = Kf - Ki

Ff = μ*m*g

Kf = 0

Ki = 0.5*m*v² = 0.5*m*2*g*Sin θ*d₁ = m*g*Sin θ*d₁

Finally

- μ*m*g*d₂ = 0 - m*g*Sin θ*d₁ ⇒ d₂ = Sin θ*d₁ / μ

3 0

4 years ago

Clare has a set of cubes with a volume of 1 cm³ each. She also has a box with a volume of 24 cm³. Exactly two layers of cubes ca

Damm [24]

Answer:

12 cubes

Step-by-step explanation:

If the total volume of the box is 24 cm³ and the volume of each cube is 1 cm³ then that means that 24 total cubes can fit perfectly inside the box. Since there can only be two layers of cubes then we simply need to divide the total amount of cubes that will fit in the box by 2 to find the number of cubes in each layer...

24 / 2 = 12 cubes

Finally, we can see that each layer within the box will contain 12 cubes

5 0

3 years ago

Evaluate ^3 sqrt 0.008- need answer asap!!

Ann [662]

∛0.008 = ∛(0.2)^3
= 0.2

hope it helps

7 0

3 years ago

The length of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the funct

Mazyrski [523]

Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.

In this case, we could say (where $A(x)$ is the area of the rectangle):

$A(x) = L(x) \cdot W(x)$

Substituting the values the problem gave us for $L(x)$ and $W(x)$ , we can find the formula for $A$ in terms of $x$ , which is:

$A(x) = (5x) \cdot (2x^2 - 4x + 13) = (10x^3 - 20x^2 + 65x)$

The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.

3 0

4 years ago

Read 2 more answers

Consider the following random experiment. First, roll a die and observe the number of dots facing up; then, toss a coin the numb

kipiarov [429]

Answer:

{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}

B.)

{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}

Step-by-step explanation:

Sample space :

Die roll, then number of coin tosses based on the outcome of the die roll, then number of heada from the toss(es) is recorded along with the outcome of the die roll.

{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}

Event that the total number of head is even:

{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}

3 0

3 years ago

The slope of the line whose equation is 3 x - 2 y = 4 is: