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Chapter 4: Problem 103

Felipe is going for a physical before joining the swim team. He is concerned about his weight, so he carries his scale into the elevator to check his weight while heading to the doctor's office on the 21 st floor of the building. If his scale reads \(750 \mathrm{N}\) while the elevator has an upward acceleration of \(2.0 \mathrm{m} / \mathrm{s}^{2},\) what does the nurse measure his weight to be?

Short Answer

Expert verified
Answer: Felipe's actual weight as measured by the nurse on the 21st floor is approximately 623.07 N.

Step by step solution

01

Determine Felipe's mass in the elevator

In order to find Felipe's mass, we can use the following equation: \(m_{elevator} = \frac{W_{elevator}}{g + a}\) where \(m_{elevator}\) is Felipe's mass in the elevator, \(W_{elevator}\) is his weight as observed in the elevator (750 N), \(g\) is acceleration due to gravity (9.81 m/s²), and \(a\) is the acceleration of the elevator (2.0 m/s²). Now, we can plug the values into the equation: \(m_{elevator} = \frac{750 \mathrm{N}}{9.81 \mathrm{m/s²} + 2.0 \mathrm{m/s²}}\)
02

Calculate Felipe's mass in the elevator

Solve the equation for \(m_{elevator}\): \(m_{elevator} = \frac{750 \mathrm{N}}{11.81 \mathrm{m/s²}} = 63.5 \mathrm{kg}\)
03

Calculate Felipe's actual weight

Now that we have Felipe's mass, we can find his actual weight by multiplying it by the acceleration due to gravity (\(g\)): \(W_{actual} = m_{elevator} \times g\) \(W_{actual} = 63.5 \mathrm{kg} \times 9.81 \mathrm{m/s²}\)
04

Calculate Felipe's measured weight by the nurse

Solve the equation for \(W_{actual}\): \(W_{actual} = 63.5 \mathrm{kg} \times 9.81 \mathrm{m/s²} = 623.07 \mathrm{N}\) So, the nurse measures Felipe's weight to be approximately 623.07 N.

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Most popular questions from this chapter

Luke stands on a scale in an elevator that has a constant acceleration upward. The scale reads \(0.960 \mathrm{kN} .\) When Luke picks up a box of mass $20.0 \mathrm{kg},\( the scale reads \)1.200 \mathrm{kN} .$ (The acceleration remains the same.) (a) Find the acceleration of the elevator. (b) Find Luke's weight.
A model rocket is fired vertically from rest. It has a net acceleration of \(17.5 \mathrm{m} / \mathrm{s}^{2} .\) After \(1.5 \mathrm{s}\), its fuel is exhausted and its only acceleration is that due to gravity. (a) Ignoring air resistance, how high does the rocket travel? (b) How long after liftoff does the rocket return to the ground?
Spring scale \(A\) is attached to the ceiling. A 10.0 -kg mass is suspended from the scale. A second spring scale, \(\mathrm{B}\), is hanging from a hook at the bottom of the 10.0 -kg mass and a 4.0 -kg mass hangs from the second spring scale. (a) What are the readings of the two scales if the masses of the scales are negligible? (b) What are the readings if each scale has a mass of $1.0 \mathrm{kg} ?$
Find and compare the weight of a \(65-\mathrm{kg}\) man on Earth with the weight of the same man on (a) Mars, where \(g=3.7 \mathrm{N} / \mathrm{kg}.\) (b) Venus, where \(g=8.9 \mathrm{N} / \mathrm{kg} ;\) and (c) Earth's Moon, where \(g=1.6 \mathrm{N} / \mathrm{kg}.\)
A toy freight train consists of an engine and three identical cars. The train is moving to the right at constant speed along a straight, level track. Three spring scales are used to connect the cars as follows: spring scale \(A\) is located between the engine and the first car; scale \(\mathrm{B}\) is between the first and second cars; scale \(C\) is between the second and third cars. (a) If air resistance and friction are negligible, what are the relative readings on the three spring scales \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C} ?\) (b) Repeat part (a), taking air resistance and friction into consideration this time. [Hint: Draw an FBD for the car in the middle. \(]\) (c) If air resistance and friction together cause a force of magnitude \(5.5 \mathrm{N}\) on each car, directed toward the left, find the readings of scales $\mathrm{A}, \mathrm{B},\( and \)\mathrm{C}$
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