The drawing shows a version of the loop-the-loop trick for a small car. The radius of the loop = 0.48 m. What is minimum initial speed () that the car needs to have in order to remain in contact with the circular track at all times?

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.

Suppose that three astronomical objects, 1, 2, and 3 are observed to lie on a line, and the distance from object 1 to object 3 is d. object 1 has four times the mass of object 3, and seven times the mass of object 2. find the distance between objects 1 and 2 for which the net force on object 2 is zero.

Awelder using a tank of volume 7.50×10^-2 m^3 fills it with oxygen (with a molar mass of 32.0 g/mol ) at a gauge pressure of 3.30×10^5 pa and temperature of 37.1 ∘c. the tank has a small leak, and in time some of the oxygen leaks out. on a day when the temperature is 23.1 ∘c, the gauge pressure of the oxygen in the tank is 2.00×10^5 pa . a) find the initial mass of oxygen. b) find the mass of oxygen that has leaked out.