# Problems of statics, angular motion and simple harmonic motion

• hjkklm
In summary, the conversation discusses various calculations and answers for different questions, including finding the correct answer for A1 and the calculated steps for A2. It also includes the sum of forces and moments for B1, as well as the calculations for kinetic energy, potential energy, and work done for B2. The conversation also covers calculations for frequency, mass, velocity, and period for B3, with the request for assistance with the last part. The speaker also asks for corrections and comments on their answers.
hjkklm
All Questions are shown on pictures.

A1(a) R= 19.21∠68.7o N
(b) E = 19.21∠-111.34o N or = -19.21∠68.7o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks.

A2(b) I = 0.5mr2 = 1.125kgm2
A2(a) k=(I/m)1/2 = 0.212m
A2(c) αt=ω, α = 3.14 rad/s2
A2(d) T=Iα = 3.53Nm

I can't gain the answer of A2(a) first. I use the A2(b) answer to help me to gain the A2(a) answer. So, the step of my calculated order is A2(b) -> A2(a) -> A2(c) -> A2(d). Is't correct?

B1(a)(ii) RBY = 1500N

sum of force and moment = 0

RA = 1200N (toward left)
RBX = 1200N (toward right)

B1(b) RBY = 500N
RA = 2012.4N (toward left)
RBX = 1146.4N (toward right)

B2(a) KE = (0.5)(10)(100) = 500J
(b) PE = (10)(9.81)(147.8) = 14503.1J
(c) v2 = {[(500 + 14503.1)x2]/10}0.5 =54.8m/s
(d ) WD = 1.2(230) = 276J , v= {[(15003.1-276)x2]/10}0.5 = 54.3m/s

B3(a) n = 1/0.08 = 12.5Hz
(b) m = (0.08/2π)2(20x103) = 3.24kg
(c) ω = 2π(12.5) = 78.5rad/s, v=78.54x0.01 = 0.785m/s
(d) f = 78.542(0.006) = 37.01m/s2 , T = 2π(0.006/37.01)0.5 = 0.08s
(e) I can't do this part, may you help me, please?

All Questions are shown on pictures.
All above my calculated ans. are correct or not? It there are something wrong, please don't hesitate to correct my answers and give some comment. Thanks a lot.

#### Attachments

• A1.JPG
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• A2.JPG
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• B1.jpg
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Questions of pictures B2 and B3

#### Attachments

• B2.JPG
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• B3.JPG
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## What is statics and why is it important in science?

Statics is the branch of mechanics that deals with the study of objects at rest or in constant motion. It is important in science because it helps us understand the forces acting on stationary objects and how they are balanced or unbalanced. This knowledge is crucial in designing structures and machines, as well as analyzing the stability and safety of objects.

## What is angular motion and how is it different from linear motion?

Angular motion is the motion of an object around a fixed point or axis. It is different from linear motion, which is the motion of an object in a straight line. In angular motion, the speed and direction of the object change constantly as it moves around the axis, while in linear motion, the speed and direction remain constant.

## What is simple harmonic motion and where is it commonly observed?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement of the object. It is commonly observed in systems such as pendulums, springs, and vibrating strings. It can also be seen in the motion of objects in circular orbits, as they experience a centripetal force that is constantly changing their direction.

## What are the key principles of statics that help us solve problems?

The key principles of statics include Newton's first law of motion (an object at rest stays at rest or in constant motion unless acted upon by an external force), Newton's second law of motion (force equals mass times acceleration), and Newton's third law of motion (for every action, there is an equal and opposite reaction). These principles help us understand the forces acting on objects and how they affect their motion.

## How does the period of a simple harmonic motion depend on its amplitude and frequency?

The period of a simple harmonic motion is the time it takes for the object to complete one full cycle of motion. It is independent of the amplitude (the maximum displacement from equilibrium) and is directly proportional to the frequency (the number of cycles per unit time). This means that as the frequency increases, the period decreases, and vice versa.

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