A boy throws a stone straight upward with an initial speed of 15m/s. What maximum height will the stone reach before falling bac

Direct tension indicators are sometimes used instead of torque wrenches to ensure that a bolt has a prescribed tension when used

natali 33 [55]

Complete Question

The complete question is shown on the uploaded image

Answer:

The tension on the shank is $T =8391.6 N$

Explanation:

From the question we are told that

The strain on the strain on the head is $\Delta l = 0.1 mm/mm = \frac{0.1}{1000} = 0.1 *10^{-3} m/m$

The contact area is $A = 2.8 mm^2 = 2.8* (\frac{1}{1000} )^2 = 2.8*10^{-6} m^2$

Looking at the first diagram

At 600 MPa of stress

The strain is $0.3mm/mm$

At 450 MPa of stress

The strain is $0.0015 mm/mm$

To find the stress at $\Delta l$ we use the interpolation method

$\frac{\sigma_{\Delta l} - \sigma_{0.0015} }{ \sigma _ {0.3} - \sigma_{0.0015} } = \frac{e_{\Delta l } - e_{0.0015}}{e_{0.3} - e_{ 0.0015}}$

Substituting values

$\frac{\sigma _{\Delta l} - 450}{600 - 450} = \frac{0.1 -0.0015}{0.3 - 0.0015}$

$\sigma _{\Delta l} -450 = 49.50$

$\sigma _{\Delta l} = 499.50 MPa$

Generally the force on each head is mathematically represented as

$F = \sigma_{\Delta l} * A$

Substituting values

$F = 499.50*10^{6} * 2.8*10^{-6}$

$=1398.6N$

Now the tension on the bolt shank is as a result of the force on the 6 head which is mathematically evaluated as

$T = 6 * F$

$= 6* 1398.6$

$T =8391.6 N$

6 0

3 years ago

Two point charges are separated by 10 cm, with an attractive force between them of 15 N. Find the force between them when they a

suter [353]

Answer:

(a) the force is 8.876 N

(b) the magnitude of each charge is 4.085 μC

Explanation:

Part (a)

Given;

coulomb's constant, K = 8.99 x 10⁹ N.m²/C²

distance between two charges, r = 10 cm = 0.1 m

force between the two charges, F = 15 N

when the distance between the charges changes to 13 cm (0.13 m)

force between the two charges, F = ?

Apply Coulomb's law;

$F = \frac{Kq_1q_2}{r^2} \\\\let \ Kq_1q_2 = C\\\\F =\frac{C}{r^2} \\\\C = Fr^2\\\\F_1r_1^2 = F_2r_2^2\\\\F_2 =\frac{F_1r_1^2}{r_2^2} \\\\F_2 = \frac{15*0.1^2}{0.13^2} \\\\F_2 = 8.876 \ N$

Part (b)

the magnitude of each charge, if they have equal magnitude

$F = \frac{KQ^2}{r^2}$

where;

F is the force between the charges

K is Coulomb's constant

Q is the charge

r is the distance between the charges

$F = \frac{KQ^2}{r^2} \\\\Q = \sqrt{\frac{Fr^2}{K} } \\\\Q = \sqrt{\frac{15*(0.1)^2}{8.99*10^9} } = 4.085 *10^{-6} \ C\\\\Q = 4.085 \ \mu C$

4 0

3 years ago

The lasers are red, meaning that they are giving off light in the _____ region of the electromagnetic spectrum

Softa [21]

As per the question the color of laser light is given as red.

If we arrange all the electromagnetic waves in the decreasing order of frequency ,then the electromagnetic spectrum contains gamma ray as the first which is followed by all other electromagnetic waves according to their frequency.

The visible light ranges from 400 nm to 700 nm which contains sunlight i.e white colors with it's constituent colors starting from violet to red. The red color is the longest wavelength part of the visible region.

The wavelength of visible light is longer than ultraviolet wave but smaller than infrared radiation. Except the bisible region,the color of radiation is invisible to eye.

As per the question the color of emiited laser radiation is red .Hence it must lie in the visible region of the electromagnetic spectrum.

4 0

3 years ago

Read 2 more answers

Match each action with the object that is primarily responsible for causing that action.

Dafna11 [192]

Moon's Orbit <u>(C). Earth</u>
Tides on Earth <u>(B). Moon</u>
Earth's Orbit <u>(A). Sun</u>

<h3>Introduction</h3>

Hi ! I will help you to explain about gravity. Gravity is one part of the force that will pull two or more objects that interact with each other to the center of their weight. Because it is a force, and interacts with mass, the gravitational force can also cause an acceleration called gravitational acceleration.The characteristic of gravity are:

Mass cannot be affected by gravitational acceleration, because mass itself has formed gravitational interactions.
The weight of an object is something that can be affected by the acceleration of gravity, because weight is a derived quantity in Newtons (N)
The lighter object will fall to the heavier object because the center of mass will be closer to the object with greater mass.

<h2>Explanation</h2>

Let's go into more detail about my answer!

<h3>Moon's Orbit</h3>

The moon undergoes two motions, orbiting the Earth and orbiting the sun together. So, here the gravitational force from the Earth can be said to have more effect on the Moon. Without the influence of Earth's gravity, the moon will orbit the sun itself by the interaction of its own gravitational force with the sun.

<h3>Tides on Earth</h3>

The tides are caused by the Moon's gravitational force. Remember ! The Earth's gravitational force always points downwards to make a constant (so that water does not spill when it is hit by the Moon's gravity). The Moon's gravitational force also depends on how close it is to Earth.

<h3>Earth's Orbit</h3>

Like the Moon, the Earth orbits the sun. However, the sun is now creating a gravitational field. Not only for Earth, but for all objects in the solar system.