Physics Dynamics Project
You are working for a company that designs ski hill runs. You have been tasked with developing a ski run with tricks for a moderately skilled skier. Assume the skier travels straight down the hill and does not take the slope gently side to side. Assume that air resistance does not slow the skier down either. The course will consist of an initial inclined hill. The skier will then go into a dip, then a hill, both modelled after semi-circles. Finally, the skier will mount a short ramp that will send them into a jump. See the picture below for a visual that is not to scale. You need to determine various dimensions to make this ski course a reality. You may need to adjust your values if the speeds or normal forces come out unrealistic.
For all calculations ensure you show free-body diagrams, formulas, plug-ins and answers to communicate your thinking clearly.
End
a) Choose the angle for your incline and the height of your hill for your large slope. Based on your chosen values, what speed will the skier have when they reach the start of the semi-circle? Do not forget to account for the friction between the skis and the snow. You will have to research an appropriate value for the frictional co-efficient. b) Choose a number that is fitting for the average mass of a skier. Choose an appropriate radius for the semi-circles. What is the skier’s apparent mass at the bottom of the dip, and at the top of the bump that follows? Why did the skier perceive a change in weight? Note: Negate friction at this step and assume the magnitude of velocity remains constant from the bottom of the hill. c) Choose an angle for the jump ramp. Choose a value for how far down vertically from the ramp the skier will land. Calculate how long the horizontal flat portion of the end of the run must be to accommodate the horizontal length of the skier’s jump. To find this value please start off using the big five kinematic equations, rather than a range equation found on the internet. See equations listed below.
d) Give an example in skiing where friction is helpful, and where it isn’t.
Equation 1: d = vt Equation 2 or, = vo + at Equation 3 = do -I- ovot + 2 ate Equation 4 , d = do + i t — lat2 Equation 5 v2 = + 2-ea
