We are going to make a model for the forces that act when you climb with...
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We are going to make a model for the forces that act when you climb with mass m fell on a joint. To simplify the problem, we shall assume that there is no external and internal friction connected to the rope and that there is no slack in the rope when the climber fell at a height h/2 above the last belay, see Figure 1. The rope has a length L (in meters m) in that case happens. All movement in the model is vertical (along the y-axis), and we shall assume that the positive direction is downwards. Figure 1: Climber with mass m falling freely in length h until the elastic rope starts to slow the fall at y = 0 and t=t0 = 0. At this point, the climber has speed v0. The rope has length L, is fixed at point S, and has no slack when the climber fell. a) The climber is in free fall until the rope starts to catch the fall. Set up the model that applies to free fall and derive the expression for the speed 10 the climber has in the rope that starts to slow the fall. In this sub-question and in sub-question d) you can assume that the speed of the climber is only a function of y so that b) In that rope, breaking the fall starts at t= t! The rope is stretched which results in a force Fb. We let y = y(t) be the length of the rope stretched at time t. Formulate an initial value problem that describes the case for t> t0 = 0 We are going to make a model for the forces that act when you climb with mass m fell on a joint. To simplify the problem, we shall assume that there is no external and internal friction connected to the rope and that there is no slack in the rope when the climber fell at a height h/2 above the last belay, see Figure 1. The rope has a length L (in meters m) in that case happens. All movement in the model is vertical (along the y-axis), and we shall assume that the positive direction is downwards. Figure 1: Climber with mass m falling freely in length h until the elastic rope starts to slow the fall at y = 0 and t=t0 = 0. At this point, the climber has speed v0. The rope has length L, is fixed at point S, and has no slack when the climber fell. a) The climber is in free fall until the rope starts to catch the fall. Set up the model that applies to free fall and derive the expression for the speed 10 the climber has in the rope that starts to slow the fall. In this sub-question and in sub-question d) you can assume that the speed of the climber is only a function of y so that b) In that rope, breaking the fall starts at t= t! The rope is stretched which results in a force Fb. We let y = y(t) be the length of the rope stretched at time t. Formulate an initial value problem that describes the case for t> t0 = 0
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