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
Artist 52 [7]
3 years ago
13

Using a forked rod, a 0.5-kg smooth peg P is forced to move along the vertical slotted path r = (0.5 θ) m, whereθ is in radians.

The angular position of the arm isθ = (π8t2) rad where t is in seconds. The peg is in contact with only one edge of the rod and slot at any instant. (Figure 1)
Part A

Determine the magnitude of the force of the rod on the peg at the instant t = 2 s.

Express your answer to three significant figures and include the appropriate units.

F =
Part B

Determine the magnitude of the normal force of the slot on the peg.

Express your answer to three significant figures and include the appropriate units.

N =

Engineering
1 answer:
-BARSIC- [3]3 years ago
4 0

Answer:

N_c = 3.03 N

F = 1.81 N

Explanation:

Given:

- The attachment missing from the question is given:

- The given expressions for the radial and θ direction of motion:

                                       r = 0.5*θ

                                       θ = 0.5*t^2              ...... (correction for the question)

- Mass of peg m = 0.5 kg

Find:

a) Determine the magnitude of the force of the rod on the peg at the instant t = 2 s.

b) Determine the magnitude of the normal force of the slot on the peg.

Solution:

- Determine the expressions for radial kinematics:

                                        dr/dt = 0.5*dθ/dt

                                        d^2r/dt^2 = 0.5*d^2θ/dt^2

- Similarly the expressions for θ direction kinematics:

                                        dθ/dt = t

                                        d^2θ/dt^2 = 1

- Evaluate each at time t = 2 s.

                                        θ = 0.5*t^2 = 0.5*2^2 = 2 rad -----> 114.59°

                                        r = 1 m , dr / dt = 1 m/s , d^2 r / dt^2 = 0.5 m/s^2

- Evaluate the angle ψ between radial and horizontal direction:

                                        tan Ψ = r / (dr/dθ) = 1 / 0.5

                                        Ψ = 63.43°

- Develop a free body diagram (attached) and the compute the radial and θ acceleration:

                                        a_r = d^2r / dt^2 - r * dθ/dt

                                        a_r = 0.5 - 1*(2)^2 = -3.5 m/s^2

                                        a_θ =  r * (d^2θ/dt^2) + 2 * (dr/dt) * (dθ/dt)

                                        a_θ = 1(1) + 2*(1)*(2) = 5 m/s^2

- Using Newton's Second Law of motion to construct equations in both radial and θ directions as follows:

Radial direction:              N_c * cos(26.57) - W*cos(24.59) = m*a_r

θ direction:                      F  - N_c * sin(26.57) + W*sin(24.59) = m*a_θ

Where, F is the force on the peg by rod and N_c is the normal force on peg by the slot. W is the weight of the peg. Using radial equation:

                                       N_c * cos(26.57) - 4.905*cos(24.59) = 0.5*-3.5

                                       N_c = 3.03 N

                                       F  - 3.03 * sin(26.57) + 4.905*sin(24.59) = 0.5*5

                                       F = 1.81 N

You might be interested in
(Signal Property) Under what condition is a discrete-time signal x[????] or a continuous-time signal x(????) periodic? Determine
Cloud [144]

Answer:

a. 2x/3

b. 8

Explanation:

fundamental period can be defined to mean that at after every period of 2π radians or 360° the value of graph is repeated. For such functions the fundamental period is the period after which they repeat themselves.

It van also be looked as The fundamental period of cos(θ) is 2π. That is (for example) cos(0) to cos(2π) represents one full period.

Please see attachment for the step by step solution.

7 0
3 years ago
Draw the ipo chart for a program that reads a number from the user and display the square of that number ???Anyone please
kompoz [17]

Answer:

See attachment for chart

Explanation:

The IPO chart implements he following algorithm

The expressions in bracket are typical examples

<u>Input</u>

Input Number (5, 4.2 or -1.2) --- This will be passed to the Processing module

<u>Processing</u>

Assign variable to the input number (x)

Calculate the square (x = 5 * 5)

Display the result (25) ----> This will be passed to the output module

<u>Output</u>

Display 25

5 0
2 years ago
Which term defines the amount of mechanical work an engine can do per unit of heat energy it uses?
skad [1K]

Answer:

d

Explanation:

is the because that's the amount of work in making machine can do producing heat

7 0
3 years ago
At steady state, air at 200 kPa, 325 K, and mass flow rate
Vera_Pavlovna [14]
Letra A

A letra

A.
Thank
3 0
3 years ago
Given: A graphite-moderated nuclear reactor. Heat is generated uniformly in uranium rods of 0.05m diameter at the rate of 7.5 x
sineoko [7]

Answer:

The maximum temperature at the center of the rod is found to be 517.24 °C

Explanation:

Assumptions:

1- Heat transfer is steady.

2- Heat transfer is in one dimension, due to axial symmetry.

3- Heat generation is uniform.

Now, we consider an inner imaginary cylinder of radius R inside the actual uranium rod of radius Ro. So, from steady state conditions, we know that, heat generated within the rod will be equal to the heat conducted at any point of the rod. So, from Fourier's Law, we write:

Heat Conduction Through Rod = Heat Generation

-kAdT/dr = qV

where,

k = thermal conductivity = 29.5 W/m.K

q = heat generation per unit volume = 7.5 x 10^7 W/m³

V = volume of rod = π r² l

A = area of rod = 2π r l

using these values, we get:

dT = - (q/2k)(r dr)

integrating from r = 0, where T(0) = To = Maximum center temperature, to r = Ro, where, T(Ro) = Ts = surface temperature = 120°C.

To -Ts = qr²/4k

To = Ts + qr²/4k

To = 120°C + (7.5 x 10^7 W/m³)(0.025 m)²/(4)(29.5 W/m.°C)

To = 120° C + 397.24° C

<u>To = 517.24° C</u>

5 0
3 years ago
Other questions:
  • Joseph wants to practice architecture. Which compulsory assessment administered by NCARB does he need to complete?
    10·1 answer
  • True or false? Engineering degree programs and engineering technology degree programs have a different requirements
    9·1 answer
  • Please what is the name of this tool​
    9·2 answers
  • Ok I need a new laptop but I'm not sure which one. The Surface laptop 3 is better in many fields like the camera, speaker, audio
    14·1 answer
  • Use the writeln() method of the document object to display the user agent in a tag in the webpage. Hint: The userAgent property
    5·1 answer
  • A cylindrical specimen of a metal alloy 45.8 mm long and 9.72 mm in diameter is stressed in tension. A true stress of 378 MPa ca
    11·1 answer
  • It describes the physical and social elements common to this work. Note that common contexts are listed toward the top, and less
    10·2 answers
  • Steam enters a heavily insulated throttling valve at 11 MPa, 600°C and exits at 5.5 MPa. Determine the final temperature of the
    14·1 answer
  • Concrete ___ support and anchor the bottom of steel columns and wood post, which support beams that are pare of framing system o
    11·1 answer
  • s) Use Cramer’s rule to solve the system below, and state the condition at which solution exists. ax+by = 1 cx+dy =−1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!