Workshop module 1 - Physics 113, Fall 1999

Workshop module 6 - Physics 113, Fall 1999

Slides on playgrounds come with sliding paths that vary in curvature and incline. In the limit of no friction, what kind of sliding board will make the child go fastest at the bottom for a given starting height? What changes if friction is present?
The earth is not a perfect sphere. The radius at the equator is approximately 21 km larger than that at the poles. So, although the source of the Mississippi River is high above sea level, it is nearer to the center of the earth than is the mouth of the Mississippi. How can this river flow "uphill"?

Young and Freedman 7-48: A skier with mass 80.0 kg starts from rest at the top of a ski slope 65.0 m high. a) Assuming negligible friction between the skis and the snow, how fast is she going at the bottom of the slope? b) Now moving horizontally, the skier crosses a patch of rough snow, where m _k = 0.20. If the patch is 225 m wide, how fast is she going after crossing the patch? c) The skier hits a snowdrift and penetrates 2.5 m into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

Young and Freedman 7-62: If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d. If the same fish is attached to the end of the unstretched spring and then allowed to fall from rest, through what maximum distance does it stretch the spring?
Can a sailboat be propelled by air blown at the sails from a fan attached to the boat?

Young and Freedman 8-25: Ken and Kim are skating together on a rink at 3.00 m/s. Ken keeps asking Kim how much she weighs. Annoyed, Kim pushes away from Ken so that she speeds up to 4.00 m/s and he slows down to 2.25 m/s in the same direction. Friction, in the physics sense, is negligible in this drama. If Ken weighs 800 N, what does Kim weigh?
Let's get a little mathematical! Young and Freedman 6-60: A force in the +x-direction has a magnitude F=b/xⁿ, where b and n are constants. a) for n>1, calculate the work done on a particle by this force when the particle moves along the x-axis from x= x₀ to infinity. b) Show that for 0<n<1, even though F becomes zero as x becomes very large, an infinite amount of work is done by F when the particle moves from x=x₀ to infinity.