A block slides down a rough ramp with a 30-degree incline as shown.

alexgriva [62]

The andwer of tye question is 3O2

6 0

3 years ago

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

4 years ago

Calculate the change in length of a Pyrex glass dish (Coefficient of linear expansion for Pyrex is 3 x 10^-6 /C) that is 0.3 met

Readme [11.4K]

Answer:

0.000225 m

Explanation:

Coefficient of linear expansion = $\alpha_L=3\times 10^{-6} /C$

Length = 0.3 meters

ΔT = Change in temperature = 250 °C

Linear expansion

$\frac{\Delta L}{L} = \alpha_L\Delta T\\\Rightarrow \Delta L=\alpha_L\Delta T\times L\\\Rightarrow \Delta L=3\times 10^{-6}\times 0.3\times 250=0.000225\ m$

Change in length of the Pyrex glass dish is 0.000225 m.

3 0

3 years ago

What is the pressure exerted by a column of fresh water 10m high (p=1000kg/m3 and g=10m/s)

alexira [117]

Height (h) = 10 m
Density (ρ) = 1000 Kg/m^3
Acceleration due to gravity (g) = 10 m/s^2
We know, pressure in a fluid = hρg
Therefore, the pressure exerted by a column of fresh water
= hρg
= (10 × 1000 × 10) Pa
= 100000 Pa

Answer:

100000 Pa

Hope you could understand.

If you have any query, feel free to ask.

8 0

3 years ago

A rectangular piece of cardboard, whose area is 352 square centimeters, is made into an open box by cutting a 2-centimeter sq

Usimov [2.4K]

Answer:

Dimension of cardboard is 22 m by 16 m

Explanation:

Given that,

Area = 352 cm²

Side of each square cutting from corner = 2 cm

Volume of box = 432 cm³

Let the two sides are x and y.

The area of the rectangular piece is

$xy=352$

$y=\dfrac{352}{x}$ -------- (1)

The volume of the rectangular piece

$2(x-4)(\dfrac{352}{x}-4)=432$

$x^2-38x+352=0$

$(x-16)(x-22)=0$

x=16,22

Put the value of x in the equation (I)

For x = 16

$y=\dfrac{352}{16}=22$

For x = 22

$y=\dfrac{352}{22}=16$

Dimension of cardboard is 22 m by 16 m

8 0

4 years ago