1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Brums [2.3K]
3 years ago
5

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

istance d_1 down the slope and then covers the distance d_2 along the horizontal terrain before stopping. Find the coefficient of kinetic friction mu_k between the sled and the ground, assuming that it is constant throughout the trip.
The coefficient is:{ d_1sin (theta)}/{d_2 + d_1cos(theta)}
To assess whether your calculations are reasonable, we'll analyze a similar situation to the one described in the problem introduction.
Suppose the same sled is released from the same height on the same slope. This time, however, assume that the coefficient of kinetic friction between the ground and the sled is a known quantity, mu, and, as before, constant throughout the trip. After the sled is released, it slides the same distance d_1 down the slope and then moves a certain (unknown) distance along the horizontal terrain before stopping. Find the distance d traveled by the sled from the end of the slope until it comes to a stop.
Express your answer in terms of the variables d_1, mu, and theta
Mathematics
1 answer:
Alenkasestr [34]3 years ago
3 0

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

<em>Distance 1:</em>

- 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   <em>(I)</em>

 

<em>Distance 2:</em>

<em />

- 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     <em>(II)</em>

<em />

<em>If we apply (I) + (II)</em>

- 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   <em>  (III)</em>

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 <em>III</em>) 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

You might be interested in
This is Sample Space. Tyra will flip a red and yellow counter and spin a spinner labeled A-E. if Tyra flips the counter and spin
Mars2501 [29]

Answer:

Just take each edge of the spinner and put it on the branches try to distribute it equally.

Step-by-step explanation:

:D

7 0
3 years ago
Write an expression for the sequence of operations described below.
aniked [119]

Answer:

It should be 9+h+2

Step-by-step explanation:

4 0
3 years ago
Which expression is equivalent to (5x^3)(2x)^3
Taya2010 [7]
Hello:
(5x^3)(2x)^3 = (5x^3)(2)^3(x)^3 = <span>(5x^3)8x^3=40x^6  ... (answer C)</span>
3 0
3 years ago
Read 2 more answers
Use the Commutative Property to write an expression equivalent to -5d + 6
Ludmilka [50]

Answer:

6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Step-by-step explanation:

Commutative Property of Addition

We know that we can add two numbers in any order.

For example,

Let 'a' and 'b' be two numbers.

We can add  'a' and 'b' numbers in any order, such as

a + b = b + a

Thus,

a + b = b + a is represented using the commutative Property of Addition.

In our case,

-5d + 6 can be written or represented using the commutative Property of Addition, such as

-5d + 6 = 6 - 5d

It is clear that -5d + 6 can be written in any order such as 6 - 5d.

In other words, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Therefore, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

7 0
2 years ago
what is an equation of the line that passes through the point (5,5) and is perpendicular to the line whose equation is y=5/9x-4
bearhunter [10]
The anwser y=-9/5x + 14
4 0
3 years ago
Other questions:
  • After Paul hiked 5/6 of a mile, he was 2/3 of the way along the trail. How long is the trail?
    7·1 answer
  • What is the height of the light pole?
    7·1 answer
  • Explain how the value of the 7 in 327,902 will change if you move it to the tens place
    5·2 answers
  • At Ezra's restaurant and bakery, each cake is cut into 9 pieces. Let c represent the number of cakes and p represent the total p
    11·1 answer
  • Is 6 and 2/3 less then 6.3?
    12·2 answers
  • Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas sto
    9·1 answer
  • Helpppppppppppppppp old!!!!!!!!!!!!
    8·2 answers
  • Pls help extra points and mark brainlist
    11·1 answer
  • What is the area of the triangle?<br> 16<br> 10<br> "T<br> 8
    8·1 answer
  • Leg = 11 meters, Hypotenuse = 15 meters
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!