Which 6 Animal exhibits will I visit?

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

Please help! Could you answer all!?

Brums [2.3K]

Answer:

1.) 48

2.) 65

3.) 36

Step-by-step explanation:

1.) If the equation is 6(x-4) and x = 12, then all we have to do is plug in the value of x. When we plug in, all we do is substitute 12 for x because they mentioned in the question that x = 12. So, we end up getting 6(12 - 4). After solving this, we get 48.

2.) This problem is a lot like the last problem. All we need to do is substitute /plug in the values of x and y into the equation, to get 4(4^2) - 35/7 - (8 + 14). After solving, we get 65.

3.) . This problem, once again, is also a lot like the last problems. We need to substitute the value of x into the equation 8x+12. Since we know from the problem that x is 3, all we have to do is 8 * 3 + 12.

3 0

3 years ago

Read 2 more answers

The shaded region in the graph represents the solutions of this system of linear inequalities:

kotegsom [21]

Answer:

$y$