Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.

Correct result:

l =  25 cm

Solution:

$$\begin{gathered} x=2\text{ cm } \\ o=20\text{ cm } \\ {o}_2=o\mathrm{/}2=20\mathrm{/}2=10\text{ cm } \\ {t}^2=o_2^2-x^2 \\ t=\sqrt{o_2^2-x^2}=\sqrt{10^2-2^2}=4\sqrt{6}\text{ cm}\doteq 9.798\text{ cm } \\ {l}^2=(l-x{)}^2+t^2 \\ {l}^2=l^2-2l_x+x^2+t^2 \\ 2l_x=x^2+t^2 \\ l=(x^2+t^2)\mathrm{/}(2\cdot x)=(2^2+9.798^2)\mathrm{/}(2\cdot 2)=25\text{ cm} \end{gathered}$$

Try another example

Showing 1 comment:

Tiny

this helps me so much

2 years ago  Like

Next similar math problems:

• Eq triangle minus arcs
  In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
• Here is
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• Flakes
  A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
• Circle section
  Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
• Square circles
  Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
• Cone A2V
  Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm². Calculate the volume of a cone.
• Cap
  Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
• Circular ring
  Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
• Circles
  In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
• Cubes
  One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm².
• Chocolate roll
  The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
• Pavement
  Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
• Two chords
  Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• Rectangle
  Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
• Cableway
  Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
• Central park in city
  The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path
• The garden
  The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?