Consider a very long, slender rod. One end of the rod is attached to a base surface maintained at Tb, while the surface of the r

Fatec – SP) Let A be a point on line r, which is contained within plane α. It holds true that: a) there is exactly one line that is perpendicular to line r at point A. b) there exists one unique line, not lying in plane α, that is parallel to line r. c) there are infinitely many distinct planes that are parallel to plane α and contain line r. d) there are infinitely many distinct planes that are perpendicular to plane α and contain line r. e) there are countless distinct lines contained within plane α that are parallel to line r.

3.941%

Response:

The cutting speed is calculated at 365.71 m/min

Clarification:

Given parameters include

diameter D = 250 mm

length L = 625 mm

Feed f = 0.30 mm/rev

cut depth = 2.5 mm

n = 0.25

C = 700

To find

the cutting speed that ensures the tool life coincides with the cutting time for the three parts

The formula for cutting time is given as

Tc =

....................1

where D refers to diameter, L refers to length and f refers to feed while V represents speed

Thus, we derive

Tc =

Tc =

Given the tool life is expressed as

T = 3 × Tc............................2

where T denotes tool life and Tc is the cutting duration

Calculating tool life by substituting values into equation 2 yields

T = 3 ×

According to the Taylor tool formula, cutting speed is expressed as

 × V × 8.37 = 700

This yields V = 365.71

Thus, the cutting speed calculates to 365.71 m/min

Response:

The solution to this question is 1273885.3 ∅

Clarification:

The first step is to ascertain the required hydraulic flow rate liquid based on the working pressure if a cylinder with a piston diameter of 100 mm is utilized.

Given that,

The distance = 50mm

The time t =10 seconds

The force F = 10kN

The piston diameter = 100mm

The pressure = F/A

10 * 10^3/Δ/Δ

P = 1273885.3503 pa

Subsequently

Power = work/time = Force * distance /time

= 10 * 1000 * 0.050/10

which amounts to =50 watt

Power =∅ΔP

50 = 1273885.3 ∅

Answer:

The duration is 17.43 minutes.

Explanation:

Based on the provided information, the initial diameter is 5 m

the velocity is 3 m/s

and the final diameter is 17 m.

To find the solution, we will use the volume change equation expressed as

ΔV = .............1

where ΔV represents the change in volume, rf is the final radius, and ri is the initial radius.

Calculating ΔV yields

ΔV =

ΔV = 2507 m³.

Thus,

Q = velocity × Area

Q = 3 × π ×(0.5)² = 2.356 m³/s.

Next, the change in time can be expressed as

Δt =

Δt =

Δt = 1046 seconds.

Therefore, the total change in time amounts to 17.43 minutes.