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
jek_recluse [69]
2 years ago
9

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

. The combined mass of monkey and sled is 14 kg, and the coefficient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move?
Mathematics
1 answer:
Aloiza [94]2 years ago
7 0

Answer:

Approximately 0.31\; \rm m, assuming that g = 9.81\; \rm N \cdot kg^{-1}.

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned} .

Weight of the slide:

\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}.

Normal force between the sled and the slope:

\begin{aligned}F_{\rm N} &= W\cdot  \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}.

Calculate the kinetic friction between the sled and the slope:

\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}.

Assume that the sled and its passenger has reached a height of h meters relative to the base of the slope.

Gain in gravitational potential energy:

\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}.

Distance travelled along the slope:

\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}.

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}.

In other words, the sled and its passenger would have lost (approximately) ((137 + 68.1)\, h)\; {\rm J} of energy when it is at a height of h\; {\rm m}.

The initial amount of energy that the sled and its passenger possessed was \text{KE} = 63\; {\rm J}. All that much energy would have been converted when the sled is at its maximum height. Therefore, when h\; {\rm m} is the maximum height of the sled, the following equation would hold.

((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}.

Solve for h:

(137 + 68.1)\, h = 63.

\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}.

Therefore, the maximum height that this sled would reach would be approximately 0.31\; \rm m.

You might be interested in
Select the correct answer.
damaskus [11]

Answer: C: Euros

Step-by-step explanation: We know it is in euros because Germany has not branched off of the EU (European Union), it still uses euros, the currency of all of the countries in the EU.

8 0
3 years ago
Read 2 more answers
The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch.
Lilit [14]

Answer:

hi how are you doing?

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Plzz helppp
dlinn [17]

Answer:

i sowwy

Step-by-step explanation:

7 0
3 years ago
Line A is represented by the following equation:
Vesnalui [34]
- for line B so the set of equations to have no solutions bc. x+y=2 and so y=2-x 
so from x+y=4 will result y=4-x

so this is the right equation for line B so the set of equations has no solutions 
6 0
3 years ago
Read 2 more answers
Need help pls question 3 pls pls pls
MaRussiya [10]

Answer:

maybe 67 ft not sure though

4 0
3 years ago
Other questions:
  •                       
    13·1 answer
  • C. what is the implied tax (i.<br> e., tax/average income) on the highest quintile?
    7·1 answer
  • On a blueprint, every 3 inches is equal to 4 feet. One of the walls of a bedroom is
    9·2 answers
  • What is p=6-2q, p=1+q, how do I use on graph
    10·1 answer
  • Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation.
    9·1 answer
  • What is the solution to 12x = 72x -192
    15·1 answer
  • Describe the relationship between complex and real numbers. Include a
    8·1 answer
  • Paul says that (3.14 x 10^5) + (2.53 x 10^4) = 5.67 x 10^5. Is Paul correct? i need a explaining
    11·1 answer
  • I will give brainliest<br> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • idc what your answer is. as long as it is related to the problem and makes sense, its based off of your opinion. (2 attachments,
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!