The steel round frame is 2,4m high. There have to be wrapd five coils around the frame. One coil diameter is 35mm. Each coil is 50m long. All of the coils have to be wrapd next to each other.What must the diameter be of the frame if the hight of the frame is 2,4m.
the circumference of the frame is πd m
The total length of wire is 5*50 = 250 m
So, ignoring the slight difference of the length of a helix as opposed to stacked rings, the number of loops around the frame is
250/πd
The height of each loop is 0.035 m, so
(250/πd)(0.035) = 2.4
d = 1.16 m
To determine the diameter of the frame, we need to consider the height of the frame and the number and length of the coils.
First, let's convert the height of the frame to centimeters (cm) for consistency. Since 1 meter (m) is equal to 100 centimeters, the height of the frame in centimeters is 2.4m * 100cm/m = 240cm.
Now, let's calculate the total length of the coils. Since there are five coils, and each coil is 50m long, the total length of the coils is 5 coils * 50m/coil = 250m.
Since the coils need to be wrapped next to each other, the total length of the coils should be equal to the circumference of the frame. The circumference of a circle can be calculated using the formula: circumference = 2 * π * radius.
We know the length (circumference) of the frame is 250m, and we need to find the radius (half of the diameter). Dividing the circumference by 2π gives us the radius.
radius = circumference / (2π) = 250m / (2 * π) = 39.79m
Finally, to find the diameter, we need to double the radius:
diameter = 2 * radius = 2 * 39.79m ≈ 79.58m
Therefore, the diameter of the frame should be approximately 79.58 meters.