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O m (Remember that the scalar mg is the weight of the fish.) Now suppose the elevator is moving with an acceleration a relative to an observer standing outside the elevator in an inertial frame (see the figure). The fish is now a particle under a net force. Apply Newton's second law to the fish. (Assume that the fish is in figure (a). Use the following as necessary: m, g, and a) EFy =T- mg = Solve for T: (1) T = ma, + mg = mg| + where we have chosen upward as the positive y-direction. We conclude from Equation (1) that the scale reading T is ---Select--- v the fish's weight mg if a is upward, so a, is positive (figure (a)), and that the reading is ---Select--- mg if a is downward, so a, is negative (figure (b)). (b) Evaluate the scale readings for a 50.0-N fish if the elevator moves with an acceleration a, = ±2.60 m/s². SOLUTION Evaluate the scale reading (in N) from Equation (1) if a is upward: T = Evaluate the scale reading (in N) from Equation (1) if a is downward: T = N Finalize Take this advice: if you buy a fish in an elevator, make sure the fish is weighed while the elevator is either at rest or accelerating downward! Furthermore, notice that from the information given here, one cannot determine the direction of the velocity of the elevator. EXERCISE Suppose that during the launch of a rocket from the surface of the Earth, an astronaut onboard the rocket stands on a bathroom scale and measures her weight to be 5.5 times her normal weight. Determine the magnitude of the acceleration of the rocket (in m/s²). Hint m/s²

O m (Remember that the scalar mg is the weight of the fish.) Now suppose the elevator is moving with an acceleration a relative to an observer standing outside the elevator in an inertial frame (see the figure). The fish is now a particle under a net force. Apply Newton's second law to the fish. (Assume that the fish is in figure (a). Use the following as necessary: m, g, and a) EFy =T- mg = Solve for T: (1) T = ma, + mg = mg| + where we have chosen upward as the positive y-direction. We conclude from Equation (1) that the scale reading T is ---Select--- v the fish's weight mg if a is upward, so a, is positive (figure (a)), and that the reading is ---Select--- mg if a is downward, so a, is negative (figure (b)). (b) Evaluate the scale readings for a 50.0-N fish if the elevator moves with an acceleration a, = ±2.60 m/s². SOLUTION Evaluate the scale reading (in N) from Equation (1) if a is upward: T = Evaluate the scale reading (in N) from Equation (1) if a is downward: T = N Finalize Take this advice: if you buy a fish in an elevator, make sure the fish is weighed while the elevator is either at rest or accelerating downward! Furthermore, notice that from the information given here, one cannot determine the direction of the velocity of the elevator. EXERCISE Suppose that during the launch of a rocket from the surface of the Earth, an astronaut onboard the rocket stands on a bathroom scale and measures her weight to be 5.5 times her normal weight. Determine the magnitude of the acceleration of the rocket (in m/s²). Hint m/s²

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O m (Remember that the scalar mg is the weight of the fish.) Now suppose the elevator is moving with an acceleration a relative to an observer standing outside the elevator in an inertial frame (see the figure). The fish is now a particle under a net force. Apply Newton's second law to the fish. (Assume that the fish is in figure (a). Use the following as necessary: m, g, and a.) Fy = T- mg = Solve for T: (1) T = may mg = mg "y + + where we have chosen upward as the positive y-direction. We conclude from Equation (1) that the scale reading T is ---Select--- v the fish's weight mg if a is upward, so a, is positive (figure (a)), and that the reading is ---Select--- v mg if a is downward, so a, is negative (figure (b)). (b) Evaluate the scale readings for a 50.0-N fish if the elevator moves with an acceleration a, = +2.60 m/s2. SOLUTION Evaluate the scale reading (in N) from Equation (1) if a is upward: T = N Evaluate the scale reading (in N) from Equation (1) if a is downward: T = N Finalize Take this advice: if you buy a fish in an elevator, make sure the fish is weighed while the elevator is either at rest or accelerating downward! Furthermore, notice that from the information given here, one cannot determine the direction of the velocity of the elevator. EXERCISE Suppose that during the launch of a rocket from the surface of the Earth, an astronaut onboard the rocket stands on a bathroom scale and measures her weight to be 5.5 times her normal weight. Determine the magnitude of the acceleration of the rocket (in m/s?). Hint m/s? Need Help? Read It
Transcribed Image Text:O m (Remember that the scalar mg is the weight of the fish.) Now suppose the elevator is moving with an acceleration a relative to an observer standing outside the elevator in an inertial frame (see the figure). The fish is now a particle under a net force. Apply Newton's second law to the fish. (Assume that the fish is in figure (a). Use the following as necessary: m, g, and a.) Fy = T- mg = Solve for T: (1) T = may mg = mg "y + + where we have chosen upward as the positive y-direction. We conclude from Equation (1) that the scale reading T is ---Select--- v the fish's weight mg if a is upward, so a, is positive (figure (a)), and that the reading is ---Select--- v mg if a is downward, so a, is negative (figure (b)). (b) Evaluate the scale readings for a 50.0-N fish if the elevator moves with an acceleration a, = +2.60 m/s2. SOLUTION Evaluate the scale reading (in N) from Equation (1) if a is upward: T = N Evaluate the scale reading (in N) from Equation (1) if a is downward: T = N Finalize Take this advice: if you buy a fish in an elevator, make sure the fish is weighed while the elevator is either at rest or accelerating downward! Furthermore, notice that from the information given here, one cannot determine the direction of the velocity of the elevator. EXERCISE Suppose that during the launch of a rocket from the surface of the Earth, an astronaut onboard the rocket stands on a bathroom scale and measures her weight to be 5.5 times her normal weight. Determine the magnitude of the acceleration of the rocket (in m/s?). Hint m/s? Need Help? Read It
Weighing a Fish in an Elevator A person weighs a fish of mass m on a spring scale attached to the ceiling of an elevator as illustrated in the figure. A fish is weighed on a spring scale in an accelerating elevator car. When the elevator accelerates When the elevator accelerates upward, the spring scale reads a value greater than the weight of the fish. downward, the spring scale reads a value less than the weight of the fish. mg mg (a) Show that if the elevator accelerates either upward or downward, the spring scale gives a reading that is different from the weight of the fish. SOLUTION Conceptualize The reading on the scale is related to the extension of the spring in the scale, which is related to the force on the end of the spring. Imagine that the fish is hanging on a string attached to the end of the spring. In this case, the magnitude of the force exerted on the spring is equal to the tension T in the string. Therefore, we are looking for T. The force T pulls ---Select--- v on the string and pulls ---Select--- v on the fish. Categorize We can categorize this problem by identifying the fish as a particle v if the elevator is not accelerating or as a particle v if the elevator is accelerating. ---Select--- ---Select--- Analyze Inspect the diagrams for forces acting on the fish in the figure and notice that the external forces acting on the fish are the downward gravitational force F, = mg and the force T exerted by the string. If the elevator is either at rest or moving at constant velocity, the fish is a particle in equilibrium, so SF, =T- F, = 0 or T = F, = Q, where Q is equal to which of the following expressions? O mg
Transcribed Image Text:Weighing a Fish in an Elevator A person weighs a fish of mass m on a spring scale attached to the ceiling of an elevator as illustrated in the figure. A fish is weighed on a spring scale in an accelerating elevator car. When the elevator accelerates When the elevator accelerates upward, the spring scale reads a value greater than the weight of the fish. downward, the spring scale reads a value less than the weight of the fish. mg mg (a) Show that if the elevator accelerates either upward or downward, the spring scale gives a reading that is different from the weight of the fish. SOLUTION Conceptualize The reading on the scale is related to the extension of the spring in the scale, which is related to the force on the end of the spring. Imagine that the fish is hanging on a string attached to the end of the spring. In this case, the magnitude of the force exerted on the spring is equal to the tension T in the string. Therefore, we are looking for T. The force T pulls ---Select--- v on the string and pulls ---Select--- v on the fish. Categorize We can categorize this problem by identifying the fish as a particle v if the elevator is not accelerating or as a particle v if the elevator is accelerating. ---Select--- ---Select--- Analyze Inspect the diagrams for forces acting on the fish in the figure and notice that the external forces acting on the fish are the downward gravitational force F, = mg and the force T exerted by the string. If the elevator is either at rest or moving at constant velocity, the fish is a particle in equilibrium, so SF, =T- F, = 0 or T = F, = Q, where Q is equal to which of the following expressions? O mg
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