Aparticle of mass 4.0 kg is constrained to move along the x-axis under a single force f(x) = −cx3 , where c = 8.0 n/m3 . the particle’s speed at a, where xa = 1.0 m, is 6.0 m/s. what is its speed at b, where xb = −2.0 m?

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20â°c throughout the year, while the walls of the room are nominally at 27â°c and 14â°c in the summer and winter, respectively. the exposed surface of a person in the room may be assumed to be at a temperature of 32â°c throughout the year and to have an emissivity of 0.90. the coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 w/m2 â‹…â‹… k. what is the ratio of the thermal resistance due to convection to the thermal resistance due to radiation in the summer? what is the ratio of thermal resistances in the winter

Follow these directions and answer the questions. 1. shine a pencil-thin beam of light on a mirror perpendicular to its surface. (if you don't have a laser light as suggested in the video, you can make a narrow beam from a flashlight by making a cone from black construction paper and taping it over the face of the flashlight.) how does the light reflect? how does the relationship of incident to reflected ray relate to the reflection of water waves moving perpendicular to a barrier? 2. shine a pencil-thin beam of light on a mirror standing on a sheet of paper on the table (or floor) so that you can mark the incident ray and reflected ray. (you can support the mirror from the back by taping it to a wooden block.) 3. mark a line on the paper representing the reflective surface. (the reflective surface of a mirror is usually the back edge.) 4. draw a dashed line perpendicular to the mirror surface at a point where the incident and reflected ray meet. this perpendicular is called a normal to the surface. 5. measure the angles between the rays and the normal. the angle of incidence is the angle formed by the incident ray and the normal to the surface. the angle formed by the reflected ray and normal is called the angle of reflection (r). what is the angle of incidence? what is the angle of reflection? 6. repeat for several different angles. (see report sheet for details.) what appears to be the relationship between the angle of incidence and angle of reflection? in science 1204, what was the relationship for these two angles made by the reflection of waves in a ripple tank? 7. roll a ball bearing so that it hits a fixed, hard surface (a metal plate) at several angles (including head-on). observe the way in which the ball bearing reflects. what generalization can you make about how a ball bearing reflects from a wall? have you proved that light can only behave like a wave?

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.