Consider a particle which is constrained to move along the surface of the sphere of radius 5, centered at the origin (a) if we write r(t) for the motion, write down the condition 'constrained to move along the surface of the sphere of radius 5 centered at the origin' in terms of r(t) b) explain why, for such a motion, we must have r'(t) r(t) (hint. differentiate c) what can you say about the acceleration? (hint. differentiate your answer from hint. for later use, try to get rid of square roots.) your answer from the previous part the previous part. draw a picture.)

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 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. a) what is the block's initial mechanical energy? 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.

Holes drilled several kilometers into earth’s crust provide direct evidence about earth’s interior in the form of

Ais a multilevel way of grouping items based on common properties among them. a. memory b. conceptual hierarchy c. schema d. semantic network