**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 μ_{k}. 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.