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Figure 6.1 Overhead view of a ball moving in a circular path in a horizontal plane. A force Fr directed toward the center of the circle keeps the ball moving in its circular path. Fig. 6.1, p.151
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Active Figure 6.2 Overhead view of a ball moving in a circular path in a horizontal plane. When the string breaks, the ball moves in the direction tangent to the circle. At the Active Figures link at you can “break” the string yourself and observe the effect on the ball’s motion. Fig. 6.2, p.152
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Figure 6.4 The conical pendulum and its free-body diagram.
Fig. 6.4, p.153
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Figure 6.4 The conical pendulum and its free-body diagram.
Fig. 6.4a, p.153
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Figure 6.4 The conical pendulum and its free-body diagram.
Fig. 6.4b, p.153
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Figure 6.5 (a) The force of static friction directed toward the center of the curve keeps the car moving in a circular path. (b) The free-body diagram for the car. Fig. 6.5, p.154
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Figure 6.6 A car rounding a curve on a road banked at an angle to the horizontal. When friction is neglected, the force that causes the centripetal acceleration and keeps the car moving in its circular path is the horizontal component of the normal force. Fig. 6.6, p.155
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Figure 6.7 (a) An aircraft executes a loop-the-loop maneuver as it moves in a vertical circle at constant speed. (b) Free-body diagram for the pilot at the bottom of the loop. In this position the pilot experiences an apparent weight greater than his true weight. (c) Free-body diagram for the pilot at the top of the loop. Fig. 6.7, p.156
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Active Figure 6.8 When the force acting on a particle moving in a circular path has a tangential component Ft, the particle’s speed changes. The total force exerted on the particle in this case is the vector sum of the radial force and the tangential force. That is, F = Fr + Ft. Fig. 6.8, p.157
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Figure 6.9 A bead slides along a curved wire.
Fig. 6.9, p.157
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Figure 6.10 (a) Forces acting on a sphere of mass m connected to a cord of length R and rotating in a vertical circle centered at O. (b) Forces acting on the sphere at the top and bottom of the circle. The tension is a maximum at the bottom and a minimum at the top. Fig. 6.10, p.158
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Figure 6.10 (a) Forces acting on a sphere of mass m connected to a cord of length R and rotating in a vertical circle centered at O. Fig. 6.10a, p.158
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Figure 6.10 (b) Forces acting on the sphere at the top and bottom of the circle. The tension is a maximum at the bottom and a minimum at the top. Fig. 6.10b, p.158
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Figure 6. 11 (a) A car approaching a curved exit ramp
Figure 6.11 (a) A car approaching a curved exit ramp. What causes a front-seat passenger to move toward the right-hand door? (b) From the frame of reference of the passenger, a force appears to push her toward the right door, but this is a fictitious force. (c) Relative to the reference frame of the Earth, the car seat applies a leftward force to the passenger, causing her to change direction along with the rest of the car. Fig. 6.11, p.159
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Active Figure 6.12 (a) You and your friend sit at the edge of a rotating turntable. In this overhead view observed by someone in an inertial reference frame attached to the Earth, you throw the ball at t = 0 in the direction of your friend. By the time tf that the ball arrives at the other side of the turntable, your friend is no longer there to catch it. According to this observer, the ball followed a straight line path, consistent with Newton’s laws. (b) From the point of view of your friend, the ball veers to one side during its flight. Your friend introduces a fictitious force to cause this deviation from the expected path. This fictitious force is called the “Coriolis force.” At the Active Figures link at you can observe the ball’s path first from the reference frame of an inertial observer, and then in the reference frame of the rotating turntable. Fig. 6.12, p.160
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Figure 6.13 A small sphere suspended from the ceiling of a boxcar accelerating to the right is deflected as shown. (a) An inertial observer at rest outside the car claims that the acceleration of the sphere is provided by the horizontal component of T. (b) A noninertial observer riding in the car says that the net force on the sphere is zero and that the deflection of the cord from the vertical is due to a fictitious force Ffictitious that balances the horizontal component of T. Fig. 6.13, p.161
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Figure 6.13 A small sphere suspended from the ceiling of a boxcar accelerating to the right is deflected as shown. (a) An inertial observer at rest outside the car claims that the acceleration of the sphere is provided by the horizontal component of T. Fig. 6.13a, p.161
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Figure 6.13 A small sphere suspended from the ceiling of a boxcar accelerating to the right is deflected as shown. (b) A noninertial observer riding in the car says that the net force on the sphere is zero and that the deflection of the cord from the vertical is due to a fictitious force Ffictitious that balances the horizontal component of T. Fig. 6.13b, p.161
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Figure 6.14 A block of mass m connected to a string tied to the center of a rotating turntable. (a) The inertial observer claims that the force causing the circular motion is provided by the force T exerted by the string on the block. (b) The noninertial observer claims that the block is not accelerating, and therefore she introduces a fictitious force of magnitude mv2/r that acts outward and balances the force T. Fig. 6.14, p.162
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Figure 6.14 A block of mass m connected to a string tied to the center of a rotating turntable. (a) The inertial observer claims that the force causing the circular motion is provided by the force T exerted by the string on the block. Fig. 6.14a, p.162
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Figure 6.14 A block of mass m connected to a string tied to the center of a rotating turntable. (b) The noninertial observer claims that the block is not accelerating, and therefore she introduces a fictitious force of magnitude mv2/r that acts outward and balances the force T. Fig. 6.14b, p.162
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Active Figure 6. 15 (a) A small sphere falling through a liquid
Active Figure 6.15 (a) A small sphere falling through a liquid. (b) Motion diagram of the sphere as it falls. (c) Speed–time graph for the sphere. The sphere reaches a maximum (or terminal) speed vT, and the time constant is the time interval during which it reaches 0.632vT. At the Active Figures link at you can vary the size and mass of the sphere and the viscosity (resistance to flow) of the surrounding medium, then observe the effects on the sphere’s motion and its speed-time graph. Fig. 6.15, p.163
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Active Figure 6. 15 (a) A small sphere falling through a liquid
Active Figure 6.15 (a) A small sphere falling through a liquid. At the Active Figures link at you can vary the size and mass of the sphere and the viscosity (resistance to flow) of the surrounding medium, then observe the effects on the sphere’s motion and its speed-time graph. Fig. 6.15a, p.163
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Active Figure 6.15 (b) Motion diagram of the sphere as it falls.
Fig. 6.15b, p.163
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Active Figure 6. 15 (c) Speed–time graph for the sphere
Active Figure 6.15 (c) Speed–time graph for the sphere. The sphere reaches a maximum (or terminal) speed vT, and the time constant is the time interval during which it reaches 0.632vT. Fig. 6.15c, p.163
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Figure 6.16 An object falling through air experiences a resistive force R and a gravitational force Fg = mg. The object reaches terminal speed (on the right) when the net force acting on it is zero, that is, when R = –Fg or R = mg. Before this occurs, the acceleration varies with speed according to Equation 6.8. Fig. 6.16, p.164
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Table 6.1, p.165
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Table 6.2, p.166
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[UN 6.3] Pleated coffee filters can be nested together so that the force of air resistance can be studied. (Charles D. Winters) Fig. 6.UN, p.166
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Figure 6.18 (a) Relationship between the resistive force acting on falling coffee filters and their terminal speed. The curved line is a second-order polynomial fit. Fig. 6.18a, p.166
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Figure 6.18 (b) Graph relating the resistive force to the square of the terminal speed. The fit of the straight line to the data points indicates that the resistive force is proportional to the terminal speed squared. Can you find the proportionality constant? Fig. 6.18b, p.166
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Figure 6.19 An object falling in vacuum under the influence of gravity.
Fig. 6.19, p.167
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Table 6.3, p.169
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Table 6.4, p.170
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Table 6.5, p.170
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Fig. P6.9, p.172
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Fig. P6.10, p.172
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Fig. P6.11, p.173
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Fig. P6.12, p.173
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Fig. P6.19, p.173
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Fig. P6.21, p.174
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Fig. P6.29, p.174
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Fig. P6.30, p.175
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Fig. P6.36, p.175
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Fig. P6.50, p.176
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Fig. P6.51, p.177
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Fig. P6.58, p.177
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Fig. P6.60, p.178
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Fig. P6.63, p.178
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Fig. P6.65, p.178
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Fig. P6.66, p.179
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Fig. P6.68, p.179
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Fig. P6.71, p.179
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Fig. QQ6.4, p.180
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Fig. QQ6.5, p.180
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