You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 99 mi/h without the aid of friction. you estimate that when elements like downforce and grip in the tires are considered, the cars will round the turns at a maximum of 175 mi/h . find the banking angle theta necessary for the race cars to navigate these turns at 99 mi/h and without the aid of friction.
this banking and radius are very close to the actual turn data at daytona international speedway where 3200 lb stock cars travel around the turns at about 175 mi/h. what additional radial force is necessary to hold the racecar on the track at 175 mi/h?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

An object of dimensions 50 cm x 40 cm x 0.20 cm has a mass 60g. find its density in g/cm3 and kg/ m3

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.