As part of your permaculture garden around your mud-brick house you need to buil
ID: 1554823 • Letter: A
Question
As part of your permaculture garden around your mud-brick house you need to build some support to grow tomato plants. Looking at the materials you have on hand you decide to use an old 2m long tent pole as the main upright and 3 ropes to make a tent style trellis. The ropes are connected to the top of the pole and then each is firmly anchored in the ground with a tent peg half a metre away from the base of the pole and equally spaced around the pole. Light weight cord is then attached between the ropes creating a framework for the tomatoes to climb up.
Towards the end of the tomato growing season you notice that each main rope is sagging under its load and at the top now makes an angle of 11 degrees with the tent pole whereas the angle was 14 degrees when you first made the trellis. You wonder what the increase in tension in each rope is due to the tomatoes and plants, and you set out to calculate this. Firstly though you need to know what forces the tomatoes and plants are applying to the trellis ropes. So you pick all of the remaining tomatoes and find you have a total of 3.75kg. Then you pull the tomato plants out, cut off the roots and weigh the plants (3.25 kg). Assume the mass was evenly distributed around the trellis and that you can make the centre of mass approximation in which the mass of tomatoes and plants can be considered to be acting at the centre of each rope. Calculate the extra tension in each half of each rope due to the tomatoes and plants.
Explanation / Answer
the total weight is = 3.75 + 3.25
= 7 kg
so the weight of each rope = 7/3
= 2.33 kg
T1 cos3 = T2 cos3 ,
T1 sin 3 + T2 sin 3 = W
T1 = T2
2 T1 sin3 = m g
= 2.33 X 9.8
T1 = 2.33 X 9.8 / 2 sin3
T1 = 218.09 N
T2 = 218.09 N
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.