Multiple-Concept Example 4 deals with a situation similar to that presented here. A marble is thrown horizontally with a speed of 18.9 m/s from the top of a building. When it strikes the ground, the marble has a velocity that makes an angle of 79∘ with the horizontal. From what height above the ground was the marble thrown? Number Units
A fire hose ejects a stream of water at an angle of 32.1∘ above the horizontal. The water leaves the nozzle with a speed of 29.4 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire? Number Units
The figure shows a Gaussian surface in the shape of a cube with edge length 1.30 m. What are (a) the net flux through the surface and (b) the net charge qenc enclosed by the surface if the electric field in the region is in the positive y direction and has a magnitude that is given by E = 4.26y N/C? What are (c) the net flux and (d) net enclosed charge if the electric field is in the xy plane and has components Ex = −4.68 N/C and Ey = (8.36 + 4.26y) N/C? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
An airplane has a mass of 2.81×104 kg and takes off under the influence of a constant net force of 2.33×104 N. What is the net force that acts on the plane's 88.1-kg pilot? Number Units
The figure below shows a Gaussian surface in the shape of a cube with edge length 1.1 m. (a) If B→ = 2.20y j^ N/C, with y in meters, what is the net flux Φ through the surface? N⋅m2/C (b) What is the net charge qenc enclosed by the surface? C (c) If E→ = −3.30i^ + (3.20 + 2.20y) j^, what is Φ? N⋅m2/C (d) What is qenc? C
The figure below shows a closed Gaussian surface in the shape of a cube of edge length 2.10 m, with one corner at x1 = 5.00 m, y1 = 4.00 m. The cube lies in a region where the electric field is given by E→ = (−3.00i^ − 4.10y2 j^ + 3.00 k^) N/C, where y is in meters. What is the net charge contained by the cube? C
A worker pushed a 32.0 kg block 11.0 m along a level floor at constant speed with a force directed 32.0∘ below the horizontal. If the coefficient of kinetic friction between block and floor was 0.220, what were (a) the work done by the worker's force and (b) the increase in thermal energy of the block-floor system? (a) Number Units (b) Number Units
The figure shows a closed Gaussian surface in the shape of a cube of edge length 1.40 m, with one corner at x1 = 5.00 m, y1 = 4.30 m. The cube lies in a region where the electric field vector is given by E→ = −3.00i^ − 3.60y2 j^ + 2.20 k^ N/C, with y in meters. What is the net charge contained by the cube? Number Units
The figure above shows a closed Gaussian surface in the shape of a cube of edge length d. It lies in a region where the electric field is given by E→ = (ax + a)i^ + bj^ + ck^. What is the net charge contained by the cube? NOTE: Express your answer in terms of the given variables using ϵ0 if necessary. q =
When released from rest, a 180 g block slides down the path shown below, reaching the bottom with a speed of 4.2 m/s. How much work does the force of friction do (in J)? J
A small block of mass 170 g starts at rest at A, slides to B where its speed is vB = 6.6 m/s, then slides along the horizontal surface a distance 13 m before coming to rest at C. (See below.) (a) What is the work of friction along the curved surface (in J)? J (b) What is the coefficient of kinetic friction along the horizontal surface?
A car loaded with your hopes and dreams has total (combined) mass of 2,500 Kg. It is set onto a ramp on a 45 degree angle and compresses a spring. The total work put into the system to load the spring is 2,400,000 J, or 2.4 Megajoules, and the end of the ramp, in meters and to one decimal place? (Ignore all friction.) (A hint: The answer is between 30 meters and 300 meters of height. Happy hunting.) (A second hint: Note I have referencing the height, not the length of the track. This is important.)