The 1 kg ball moves with the parabolic bowl rotating at constant speed around a vertical axis (the ball is immobile relative to the bowl). Friction is neglected and if r = 1 m, a) ball velocity v b) Find the magnitude of the normal force exerted on the ball by the inclined plane.

(a) What happens to the gravitational force between two objects if their separation is doubled? (b) Two objects with masses of m,= 5 kg and m2= 8 kg are connected by a light string that passes over a frictionless pulley, as in figure. Determine (i) the acceleration of each object, (ii) the tension in the string and (iii) the distance each object will move in 0.8 s of motion if both objects start from rest. m2

A black aluminum glider floats on a film of air above a level aluminum air track. Aluminum feels essentially no force in a magnetic field, and air resistance is negligible. A strong magnet is attached to the top of the glider, forming a total mass of 240 g. A piece of scrap iron attached to one end stop on the track attracts the magnet with a force of 0.823 N when the iron and the magnet are separated by 2.50 cm. (a) Find the accelerationof the glider at this instant. (b) The scrap iron is now attached to another green glider, forming total mass 120 g. Find the acceleration of each glider when the gliders are simultaneously released at 2.50-cm separation.

A daredevil bicyclıst moves at 7.0m/s in a horizontal cirde in a cylindrical "weli of dea th" of radius 4.0 m. (A.) Draw the free - bady diagram (B) What is the minimum coefficient of friction required ? man riding a bike

A block of mass m = 1 kg is found on an inclined plane that makes an angle 30° with the horizontal. The coefficient of static friction and coef- ficient of kinetic friction between the block and the incline are: u, = 0.6 and uk = 0.5. Take the positive di- rection to be up the inclined plane 130° With the block initially at rest, the acceleration of the block is

In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass m riding around a horizontal circle of radius r at speed v.What is the variation dF in the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the speed with r held constant, and (c) a variation dT in the period with r held constant?

B of mass Car A of mass m is driving with a speed 2v on a road with radius of curvature R. Car 2m is driving with a speed v on the same road. Assume that the only force in the normal direction is the force of friction. By what factor does the required force of friction vary from car A to car B so that the cars do ot slide out?

A  7.4 -kg rock and a  8.0  × 10-4-kg pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the magnitude of the acceleration of each object when released.