Example 7.6A Block Pulled on a Frictionless SurfaceA 8.3-kg block initially at rest is pulled to the right alonga frictionless, horizontal surface by a constant horizontalforce of magnitude 36 N. Find the block's speed after ithas moved through a horizontal distance of 7.0 m.SOLVE ITConceptualize The figure illustrates this situation.Imagine pulling a toy car across a table vith a horizontalrubber band attached to the front of the car. The force ismaintained constant by ensuring that the stretchedrubber band always has the same length.A block pulled to the right on a frictionlesssurface by a constant horizontal force.Categorize We could apply the equations of kinematicsto determine the answer, but let us practice the energy approach. The block is the system, and threeexternal forces act on the system. The normal force balances the gravitational force on the block, andneither of these vertically acting forces does work on the block because their points of application arehorizontally displaced.Analyze The net external force acting on the block is the horizontal 36-N force.Use the work-kinetic energy theorem forthe block, noting that its initial kineticWe = AK = K, - K, = mv - 0 =mvenergy is zero:Solve for v, and use W = FAr cos 8 for the2West.2FAXmwork done on the block by F:Substitute numerical values:2(36 N)(7.0 m)8.3 kgm/sFinalize You should solve this problem again by modeling the block as a particle under a net force to findits acceleration and then as a particle under constant acceleration to find its final velocity. In a follovingchapter, we will see that the energy procedure followed above is an example of the analysis model of thenonisolated system.MASTER ITHINTS:GETTING STARTED I I'M STUCK!For the above example, suppose that the magnitude of the force is doubled. Through what displacementwill the block travel before reaching the same final speed found above?ח A particle moving in the xy plane follows a path described as a function of time by i(t) = (3.4 m/s)tî -(2.8 m/s?)tj. A constant force given by F = (5.0î - 2.0j) N acts on the particle (note that other forcesmust act on the particle as well if it follows the path given above).(a) Determine the displacement of the particle during the interval t = 1.0 s to t = 4.0 s.AT =îm -m(b) Calculate the work done by F during this interval.W =

Note: As there is more than one question, as per the policy, only the first question can be solved.…

Example 7.6 A Block Pulled on a Frictionless Surface A 8.3-kg block initially at rest is pulled to the right along a frictionless, horizontal surface by a constant horizontal force of magnitude 36 N. Find the block's speed after it has moved through a horizontal distance of 7.0 m. SOLVE IT Conceptualize The figure illustrates this situation. Imagine pulling a toy car across a table vith a horizontal rubber band attached to the front of the car. The force is maintained constant by ensuring that the stretched rubber band alvays has the same length. A block pulled to the right on a frictionless surface by a constant horizontal force. Categorize We could apply the equations of kinematics to determine the answer, but let us practice the energy approach. The block is the system, and three external forces act on the system. The normal force balances the gravitational force on the block, and neither of these vertically acting forces does work on the block because their points of application are horizontally displaced. Analyze The net external force acting on the block is the horizontal 36-N force. Use the work-kinetic energy theorem for Wa - AK = K, - K, -mv? - 0 =mv; the block, noting that its initial kinetic energy is zero: Solve for v, and use w Far cos 8 for the 2FAX work done on the block by F: m 2(36 N)(7.0 m) 8.3 kg Substitute numerical values: m/s Finalize You should solve this problem again by modeling the block as a particle under a net force to find its acceleration and then as a particle under constant acceleration to find its final velocity. In a following chapter, we will see that the energy procedure followed above is an example of the analysis model of the nonisolated system. MASTER IT GETTING STARTED I IMSTUCK HINTS: For the above example, suppose that the magnitude of the force is doubled. Through what displacement will the block travel before reaching the same final speed found above? m