Elevator

In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft
engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the counterweight.

Consider lift-enabled load Mmax = 300 kg
car weight mk = 500 kg
weight counterweight mz = 650 kg. Cabin moves at the speed
v0 = 1.2 m/s. The total efficiency of power is k =75%.

a) Explain what affects the efficiency of the system and the reason for using a counterweight.

b) Determine the power P1 engine lift if you summon an empty cabin residents of the upper floors, which moves down the speed of v0.
c) Determine the power P2 engine lift when a group of citizens with a total mass M = 250 kg conveys speed v0 upwards.

In which of these cases b), c) the need for more power?
g = gravitational constant 10 N/kg

Correct result:

P1 =  2.4 kW
P2 =  1.6 kW

Solution:

P1=mkmzgv010075 P1=500650101.210075=2.4 kWP_1 = |m_k-m_z|g v_0 \dfrac{ 100 }{ 75 } \ \\ P_1 = |500-650| 10 \cdot 1.2 \dfrac{ 100 }{ 75 } = 2.4 \ \text{kW}
P2=mk+Mmzgv010075 P2=500+250650101.210075=1.6 kW P1>P2P_2 = |m_k+M-m_z|g v_0 \dfrac{ 100 }{ 75 } \ \\ P_2 = |500+250-650| 10 \cdot 1.2 \dfrac{ 100 }{ 75 } = 1.6 \ \text{kW} \ \\ P_1 > P_2



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

Next similar math problems:

  • Granddaughter
    calendar In 2014, the sum of the ages of Meghan's aunt, her daughter and her granddaughter was equal to 100 years. In what year was the granddaughter born, if we know that the age of each can be expressed as the power of two?
  • Cube V2S
    cube_shield The volume of the cube is 27 dm cubic. Calculate the surface of the cube.
  • Cube surfce2volume
    cube_shield Calculate the volume of the cube if its surface is 150 cm2.
  • Spherical segment
    SphericalSegment_1000 Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
  • Cuboid to cube
    cube_shield_1 A cuboid with dimensions of 9 cm, 6 cm, and 4 cm has the same volume as a cube. Calculate the surface of this cube.
  • Eight
    sphere_in_cube Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls, or one big ball?
  • Magnified cube
    cube_in_sphere If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
  • The half life
    exp_growth2 The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives?
  • An example
    cubes3_2 An example is playfully for grade 6 from Math and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: A cuboid was made from a block of 16x18x48 mm of modeline. What will be the edge of t
  • Cardboard box
    karton_krabica Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
  • Cuboid and ratio
    cuboid_2 Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
  • Wall thickness
    sphere_Nickel The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
  • The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  • One third power
    cube-root Which equation justifies why ten to the one-third power equals the cube root of ten?
  • Length of the edge
    cube_shield Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
  • Three members GP
    exp_growth The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
  • Cube into cylinder
    cube_sphere_in If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?