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 rat speed v. what is the variation df in the net force magnitude for(a) a variation dr in the radius with ν 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?

If you were to drop a rock from a tall building, assuming that it had not yet hit the ground, and neglecting air resistance. what is its vertical displacement (in m) after 6 s?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Blank liquids and gases exert a buoyant force on objects placed in them