Assignment 1

Problem 1:

A highway curve with a radius of 750 m is banked properly for a car traveling 120 km/h.  If a 1590 kg Porsche rounds the curve at 230 km/h,
(a)  how much sideway force must the tires exert against the road if the car does not skid?
(b)  what must be the bank angle for the Porsche to turn if there is no friction force on the tires?

Problem 2:

The shortest way from the US to Australia is via a tunnel that goes thought the center of the Earth.  If one could build such a tunnel and make it friction free, then an object dropped at the US side with zero initial velocity would emerge after some time on the other side in Australia.  Assuming that density of the Earth is uniform (which is not correct), calculate how long it would take for an object to pass through such a tunnel. 

Problem 3:

A block is given a quick push along a horizontal table.  The coefficient of kinetic friction between the block and the table is μk.  It is known that during the time interval t (immediately after the push) the block covers a distance d.  Find the distance that may be covered by the block during the subsequent time interval t'.  Find all possible answers.

Problem 4:

Two wedges are placed mirror symmetrically so that the tip of one touches the tip of another as shown in the figure below.  The surface of each wedge is at angle θ = 30 degrees relative to the ground.  A small elastic ball is dropped from height h = 1 m with zero initial velocity.  How far from the tips of the two wedges (x) must the small ball be dropped, so that after bouncing from the two wedges it will reach the same height from where it was dropped?  Neglect any friction from air and consider the bouncing of the ball to be completely elastic.

Problem 5:

A brave physics student (an undergraduate, of course) climbs aboard a high powered merry-go-round and goes to the center, at r = 0.  At time t = 0, the platform starts from rest (Ω = 0) and begins to spin about its vertical axis with constant angular acceleration α.  Also at time t = 0, the student begins to crawl radially outward at constant speed v, relative to the platform.
Assuming the student does not slip, find the student's acceleration in the inertial frame of an outside observer.