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
marishachu [46]
3 years ago
5

You are in a helicopter towing a 125-kg laser detector that mapping out the thickness of the Brunt Ice Shelf along the coast of

Antarctica The original cable used to suspend the detector was damaged and replaced by a lighter one with a maximum tension rating of 305 pounds, not much more than the weight of the detector. The replacement cable would work without question in the case that the detector and helicopter were not accelerating . However, some acceleration of the helicopter is inevitableIn order to monitor the tension force on the cable to make sure the maximum is not exceeded (and therefore to not lose the very expensive detector ) you calculate the maximum angle the cable can make with the vertical without the cable exceeding the tension limit Assuming straight and level of the helicopter, what is that maximum angle? () What is the corresponding acceleration? ( c) Your colleague wants to add a 10.0 kg infrared camera to the detector. What is the maximum allowable angle now?

Physics
1 answer:
Alexxx [7]3 years ago
6 0

Answer:

(a) \theta=25.45^o

(b) a=4.665\ m/s^2

(c) \theta'=12.80^o

Explanation:

<u>Accelerated Motion</u>

The kinematic conditions of an object that is subject to forces are mathematically described by Newton's laws, specifically, the second law where the net force Fn can be calculated if we know the mass of the object m and its acceleration a by the relation

F_n=m.a

The net force can be also calculated by adding all the vector forces applied to the object. This procedure can be used to compute the acceleration of the object, given the forces acting on it.

In our problem, we have a m=125 Kg laser detector that is being pulled out by a cable of maximum tension T=305 lb-f from a helicopter. As the helicopter moves, the cable makes a vertical angle \theta that must be kept at some limit when the helicopter accelerates in such a way the cable won't break.

The free-body diagram is shown in the figure below. The equilibrium equation for the y-axis is:

Tcos\theta-W=0

Rearranging

Tcos\theta=W

We assume there is no acceleration in the vertical direction

Similarly, the equilibrium equation for the x-axis is

Tsin\theta=m.a

(b) To find the acceleration we must eliminate the angle from the system of equations, we do that by squaring both and adding them term by term:

(Tcos\theta)^2+(Tsin\theta)^2=W^2+(m.a)^2

Operating and knowing that W=m.g

T^2cos^2\theta+T^2sin^2\theta=m^2(g^2+a^2)

Since sin^2\theta+cos^2\theta=1

T^2=m^2(g^2+a^2)

Solving for a

\displaystyle a=\frac{1}{m}\sqrt{T^2-W^2}

The maximum tension is

T=305\ lbf=1356.71 Nw

The Weight is

W=125 \cdot 9.8=1225\ Nw

Plugging in the values

\displaystyle a=\frac{1}{125}\sqrt{1356.71^2-1225^2}

a=4.665\ m/s^2

(a) To find the angle, we divide the second equation by the first equation:

\displaystyle \frac{Tsin\theta}{Tcos\theta}=\frac{m.a}{m.g}

Simplifying

\displaystyle tan\theta=\frac{a}{g}=\frac{4.665}{9.8}=0.476

Which gives us an angle

\theta=25.45^o

(c) If an additional mass of 10 kg was added to the infrared camera, the new weight would be

W'=(125+10)\cdot 9.8=1323\ Nw

The new maximum acceleration is now

\displaystyle a'=\frac{1}{135}\sqrt{1356.71^2-1323^2}

a'=2.226\ m/s^2

With a maximum angle of

\displaystyle tan\theta'=\frac{2.226}{9.8}=0.227

\theta'=12.80^o

You might be interested in
An athletes heart beats 62 times per minute. What is the frequency of her heart beat?
PilotLPTM [1.2K]

Answer:

22

Explanation:

bc it just is

8 0
3 years ago
What usually results when an organism fails to maintain homeostasis?
dedylja [7]
The organism may become ill or die
3 0
3 years ago
Read 2 more answers
Conversion fraction 1$=4q, how many are in 20$
Tom [10]

Answer:

\boxed{\sf 20 \$ = 80q}

Given:

1$ = 4q

To Find:

How many quarters are in 20$

Explanation:

To find out how many quarters are in 20$ we need to multiple 4 × 20.

\sf 1\$  = 4q

\sf  20\$  = 4 \times 20q

\sf = 80q

8 0
3 years ago
Read 2 more answers
The potential difference across a and b is 15 v. determine the electrical charge on the 3 μf capacitor?
Slav-nsk [51]

The potential difference across a and b is 15 v. determine the electrical charge on the 3 μf capacitor will be 45 *  10^{-6} C

Capacitance, property of an electric conductor, or set of conductors, that is measured by the amount of separated electric charge that can be stored on it per unit change in electrical potential. Capacitance also implies an associated storage of electrical energy.

Charge (Q) stored in a capacitor is the product of its capacitance (C) and the voltage (V) applied to it. The capacitance of a capacitor should always be a constant, known value. So we can adjust voltage to increase or decrease the cap's charge. More voltage means more charge, less voltage... less charge.

charge = capacitance * voltage

Q = CV

   =  3  * 10^{-6} * 15 v

   = 45 *  10^{-6} C

To learn more about capacitance here

brainly.com/question/14746225

#SPJ4

8 0
2 years ago
A ball is projected upward at time t=0.0s, from a point on a roof 90m above the ground. The ball rises, then falls and strikes t
chubhunter [2.5K]
As v becomes zero at the highest point, i prefer considering different travelling directions so it will become less complicated.
dont forget to add the total time up .

also to master the skills, write down the "uvsat" may help (thats the way i found it easier to handle problems)

4 0
3 years ago
Other questions:
  • Why do bolt cutters have long handles and short blades laws of physics?
    6·1 answer
  • Amber applies a net force of 35 N to pull her younger brother (32 kg) in a wagon (3 kg). at what rate does the wagon accerlerate
    7·1 answer
  • How do you find the g field at a point between 2 masses?
    12·1 answer
  • a. Of the three experiments that are used to confirm the Big Bang theory, which is the most interesting to you and why?
    7·1 answer
  • Light of wavelength 600 nm passes though two slits separated by 0.25 mm and is observed on a screen 1.4 m behind the slits. The
    8·2 answers
  • Is ADa is civil rights
    6·1 answer
  • ________ is a measure of the internal energy that has been absorbed or transferred from one body to another, often due to a diff
    8·1 answer
  • If you were an Astronaut in the middle of the near side of the moon during a full moon, how would the ground around you look? Ho
    8·1 answer
  • Can someone help me find the answer?
    11·2 answers
  • Read the claim about caffeine. Caffeine improves mental alertness and motor coordination. A university research study was conduc
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!