A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and freuency of 2.55 Hz.(a) what's the maximum speed of the needle ?
(b) what's the maximum acceleration of the needle ?

Answers

Answer 1

Answer:

Answer:

The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.

Explanation:

Given that,

Frequency = 2.5 Hz

Amplitude = 1.27 cm

(a). We need to calculate the time

The frequency is the reciprocal of the time.

The time taken from highest point to lowest point

(b). We need to calculate the time

The time taken in one cycle = 0.4 sec

The distance covered in one sec= 4 times x amplitude

We need to calculate the speed

Using formula of speed

We need to calculate the time

Hence, The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.

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State whether these questions are true or false.Q1) Distance formula is displacement/time T/F?
Q2)velocity formula is = displacement/time T/F?

Answers

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The given statements are :

Q1) Distance formula is displacement/time T/F?

- False

Q2)velocity formula is = displacement/time T/F?

- True

The temperature of 20 liters of helium gas is increased from 100°K to 300°K. If the pressure was kept constant, the new volume will be how many liters? a) 6.7 b) 30 c) 60 d) 120 e) None of these

Answers

Answer:

New volume (V2) = 60 liter

Explanation:

Given:

Amount of helium (V1) = 20 Liter

Temperature (T1) = 100°K

Temperature (T2) = 300°K

Find:

New volume (V2)

Computation:

According to Gas Law:

V1 / T1 = V2 / T2

20 / 100°K = V2 / 300°K

V2 = 60 liter

New volume (V2) = 60 liter

The asthenosphere is a part of the upper mantle just below the lithosphere that is involved in plate tectonic movement and isostatic adjustments. Which is NOT true about the role of the asthenosphere in plate tectonics?

Answers

Complete option to the question:

A. The asthenosphere is broken up into large continental- and ocean-sized plates.

B. Convection currents within the asthenosphere push magma upward to create new crust.

C. Heat from deep within Earth is thought to keep the asthenosphere malleable.

D. The asthenosphere is the repository for parts of the lithosphere that are dragged downward in subduction zones.

Answer: The correct option is A (The asthenosphere is broken up into large continental- and ocean-sized plates.)

Explanation:

Among the components that makes up the earth crust are the lithosphere and the asthenosphere.

The LITHOSPHERE is the outer layer of the earth structure which consists of the upper part of the mantle and the crust.

The ASTHENOSPHERE is a part of the upper mantle just below the lithosphere that is involved in plate tectonic movement and isostatic adjustments. It is denser and weaker layer of the upper mantle which permits the movement of tectonic plates in the lithosphere.

The asthenosphere is the repository for parts of the lithosphere that are dragged downward in subduction zones.Heat from deep within Earth is thought to keep the asthenosphere malleable. And the convection currents within the asthenosphere push magma upward to create new crust. But it is not broken up into large continental- and ocean-sized plates.

What is distance and direction of an object from its starting point

Answers

The distance and direction of an object from its starting point is called displacement. The main difference between distance and displacement is the consideration of distance in displacement. Distance is a scalar quantity, while displacement is a vector quantity. Scalar quantities don't take note of direction, while vector quantities do.

BAlpha Centauri has an apparent magnitude of -0.27, whereas the apparent
magnitude of Alpha Crucis is 0.77. Identify which star appears brighter when observed from
Earth. Explain your answer.

Answers

Answer:

Alpha centauri will be brighter than Alpha Crucis .

Explanation:

Apparent magnitude of a star measures how bright a star is .

This scale is reverse logarithmic ie , the brighter the star , the lower is its magnitude . A magnitude equal to 5 scale higher represents less magnitude by a factor of 1/ 100 . In this way a difference of 1 magnitude represents a brightness ratio of 2.512 . Hence a star of brightness magnitude of 7 is less bright by a factor 2.512 than that of a star magnitude of 6 .

A puck moves 2.35 m/s in a -22° direction. A hockey stick pushes it for 0.215 s, changing its velocity to 6.42 m/s in a 50.0° direction. What was the direction of the acceleration?

Answers

The puck starts with velocity vector

$\vec v_0=\left(2.35(\rm m)/(\rm s)\right)(\cos(-22^\circ)\,\vec\imath+\sin(-22^\circ)\,\vec\jmath)=(2.18\,\vec\imath-0.880\,\vec\jmath)(\rm m)/(\rm s)$

Its velocity at time $t$ is

$\vec v=\vec v_0+\vec at$

Over the 0.215 s interval, the velocity changes to

$\vec v=\left(6.42(\rm m)/(\rm s)\right)(\cos50.0^\circ\,\vec\imath+\sin50.0^\circ\,\vec\jmath)=(4.13\,\vec\imath+4.92\,\vec\jmath)(\rm m)/(\rm s)$

Then the acceleration must have been

$\vec v=\vec v_0+(0.215\,\mathrm s)\vec a\implies\vec a=(\vec v-\vec v_0)/(0.215\,\rm s)=(9.06\,\vec\imath+27.0\,\vec\jmath)(\rm m)/(\mathrm s^2)$

which has a direction of about $71.4^\circ$ .

Final answer:

The direction of the acceleration is determined by the direction of the change in velocity. This would be calculated by subtracting the initial velocity vector from the final velocity vector. However, the calculation would involve complex trigonometric functions.

Explanation:

In order to find the direction of the acceleration, we need to calculate the direction of the change in velocity and that direction will be the direction of the acceleration.

To calculate the change in velocity, we subtract the initial velocity from the final velocity: (6.42 m/s, 50.0°) - (2.35 m/s, -22°). We then calculate the angle of this vector which represents the change in velocity, and hence the direction of acceleration.

However, this calculation is not straightforward because it involves vector operations and would require the use of trigonometric functions to solve. This is due to the fact that velocity is a vector, meaning it has both a magnitude and a direction. Consequently, this becomes a multi-step process involving trigonometry and physics.