V-belt

Calculate a length of the V-belt when the diameter of the pulleys is:

D1 = 600 mm
D2 = 120 mm
d = 480 mm

Result

l =  2185 mm

Solution:

d1=600 mm d2=120 mm d=480 mm  r1=d1/2=600/2=300 mm r2=d2/2=120/2=60 mm  a=r1r2=30060=240 mm  A=arctan(a/d)=arctan(240/480)0.4636 rad  A1=π+2 A=3.1416+2 0.46364.0689 rad A2=π2 A=3.14162 0.46362.2143 rad  l1=r1 A1=300 4.06891220.6664 mm l2=r2 A2=60 2.2143132.8578 mm  b=d2a2=48022402=240 3 mm415.6922 mm  l=l1+l2+2 b=1220.6664+132.8578+2 415.69222184.9086=2185  mm d_{ 1 } = 600 \ mm \ \\ d_{ 2 } = 120 \ mm \ \\ d = 480 \ mm \ \\ \ \\ r_{ 1 } = d_{ 1 }/2 = 600/2 = 300 \ mm \ \\ r_{ 2 } = d_{ 2 }/2 = 120/2 = 60 \ mm \ \\ \ \\ a = r_{ 1 } - r_{ 2 } = 300 - 60 = 240 \ mm \ \\ \ \\ A = \arctan(a/d) = \arctan(240/480) \doteq 0.4636 \ rad \ \\ \ \\ A_{ 1 } = \pi + 2 \cdot \ A = 3.1416 + 2 \cdot \ 0.4636 \doteq 4.0689 \ rad \ \\ A_{ 2 } = \pi - 2 \cdot \ A = 3.1416 - 2 \cdot \ 0.4636 \doteq 2.2143 \ rad \ \\ \ \\ l_{ 1 } = r_{ 1 } \cdot \ A_{ 1 } = 300 \cdot \ 4.0689 \doteq 1220.6664 \ mm \ \\ l_{ 2 } = r_{ 2 } \cdot \ A_{ 2 } = 60 \cdot \ 2.2143 \doteq 132.8578 \ mm \ \\ \ \\ b = \sqrt{ d^2-a^2 } = \sqrt{ 480^2-240^2 } = 240 \ \sqrt{ 3 } \ mm \doteq 415.6922 \ mm \ \\ \ \\ l = l_{ 1 } + l_{ 2 } + 2 \cdot \ b = 1220.6664 + 132.8578 + 2 \cdot \ 415.6922 \doteq 2184.9086 = 2185 \ \text { mm }







Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Do you want to convert length units? See also our right triangle calculator. See also our trigonometric triangle calculator.

Next similar math problems:

  1. A boy
    angles_6 A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
  2. Aircraft
    aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
  3. Church tower
    usti-kostel Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
  4. Pyramid
    jehlan Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
  5. Chord
    chord_1 Point on the circle is the end point of diameter and end point of chord length of radius. What angle between chord and diameter?
  6. The mast
    geodet_1 The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
  7. Mast shadow
    horizons Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
  8. The Eiffel Tower
    Eiffel-Tower-Paris The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
  9. Trapezium ABCD
    lichobeznik_5 In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
  10. Hole's angles
    Trapezium2-300x199 I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)?
  11. Maple
    tree_javor Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
  12. Trapezoid - RR
    right_trapezium Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
  13. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  14. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  15. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  16. High wall
    mur I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?