Question 5 We'll now investigate the concept of a space elevator-a potentially much more efficient way to get to space. First. let's think about how the tension in a rope varies. Imagine you are holding the top of a piece of rope. and letting it dangle down. Where in the rope is the tension highest? (hint- remember that fumes must balance not just for the whole rope but for any part of it}. Select one: Select one: O At the top of the rope O At the middle of the rope O At the bottom of the rope The tension at the top of the rope must support the weight of all the rope below. Write down an equation for the weight of a rope of length L and cross-sectional area A. This must be equal to the tension force. Divide by the cross-sectional area to get an equation for the tension force per unit cross-sectional area. Rearrange this equation to get the maximum possible length for a given maximum tension per unit area. Nylon rope has a density of 1300 kg per cubic metre and a maximum tension per unit area of >( 1.03 N m_2- What is the maximum length of a nylon rope before it breaks due to its own weight? [in kilometres} Answer: Question 5 The idea behind a space elevator is to put a satellite in orbit and lower a cable down from it until it reaches the Earth's surface, where it is bolted down. Astronauts will ride elevator cars up the side of this cable to get to space. https:.-';'en.wikipedia.orgfwikifSpacejlevator What sort oforbit should the satellite be in. from which the cable is lowered? Select one: Select one: C) An orbit that passes over both poles, exactly twice a day. Q The lowest orbit possible. to minimise the length of the cable C) An orbit over the Earth's equator with an orbital period of ~24 hours. C) An orbit hovering over either the north or south poles A geostationary orbit is 36,000 km above the Earth surface. As we saw in Question 4. 36,000 km is much longer than the maximum length of a nylon rope. However, in calculating the maximum length of a rope. we assumed that gravity was constant along the rope. For a space elevator, gravity is much weaker as you go up. In addition, centrifugal force helps support the upper parts of the elevator. So the main challenge is supporting the lower parts of the elevator cable. where gravity is still strong and centrifugal force weak. Let's get a rough estimate of the strength required. Let's make the approximation that the bottom 5,000 km of the cable is exposed to full g gravity (Le. the same as at the Earth*s surface} and negligible centrifugal force. But then we will assume that the rest of the cable has no net gravity. Both these assumptions are wrong, but one will make the tension higher while the other makes it lower. so together they will probably give us a reasonable estimate. to within a factor of 2-3. This is enough to tell us if this idea is even vaguely possible. And if it is, we can do a more detailed calculation {which we actually do later in the course}. Imagine the cable was made of carbon nanotubes. Given our assumptions, what tensile strength (in mega-pascals} is needed to support such a space elevator? So our rough calculation comes out close to the actual maximum tensile strength of carbon nanotubes. So-we can't build a space elevator out of steel or nylon rope. but it is not completely impossible-carbon nanotubes might just about do it. Though a more detailed calculation would be needed to be sure. Even if we can't build a space elevator on Earth, maybe it would be easier on another planet. On what type of planet would it be easiest to build a space elevator? Select one: Select one: O A low mass planet with a short day 0 A low mass planet with a long day O A high mass planet with a short day O A high mass planet with a long day