Concept explainers
Physicians and physiologists are interested in the long-term effects of apparent weightlessness on the human body. Among these effects are redistribution of body fluids to the upper body, loss of muscle tone, and overall mass loss. One method of measuring mass in the apparent weightlessness of an orbiting spacecraft is to strap the astronaut into a chairlike device mounted on springs (Fig. 13.39). This body mass measuring device (BMMD) is set oscillating in simple harmonic
FIGURE 13.39 Astronaut Tamara Jernigan uses a body mass measuring device in the Spacelab Life Sciences Module (Passage Problems 87-90).
motion, and measurement of the oscillation period, along with the known spring constant and mass of the chair itself, then yields the astronaut’s mass. When a 60-kg astronaut is strapped into the 20-kg chair, the time for three oscillation periods is measured to be 6.0 s.
The spring constant for the BMMD described here is
- a. 80 N/m.
- b. 80π N/m.
- c. 2 N/m.
- d. 80π2 N/m.
- e. none of the above.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Additional Science Textbook Solutions
Physics (5th Edition)
Introduction to Electrodynamics
Cosmic Perspective Fundamentals
Life in the Universe (4th Edition)
Sears And Zemansky's University Physics With Modern Physics
Conceptual Physics (12th Edition)
- In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.arrow_forwardWe do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.arrow_forwardFor each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3arrow_forward
- The period of a simple pendulum (T) is measured as a function of length (L) on an unknown planet. The dependence of of L is linear (see the graph below). Use the slope of this graph to calculate the acceleration of gravity on this planet, in m/s2. 0.25 y = 0.0909x 0.2 0.15 0.1 0.05 Plot Area 0.5 1 1.5 2 2.5 L (m) T?/4 pi?(s')arrow_forwardA simple oscillating motion is solved by the equation x (t) = 0.35 cos (15.0 · t + 0.60) ar where all quantities are in SI units and angles are measured in radians. (a) Find the highest velocity in the oscillation. At what value of x is the velocity greatest? (b) What is the greatest acceleration in the oscillation? At what value of x will the acceleration be greatest?arrow_forwardIt is important to remember that, in a real pendulum, the value of L used in the period equation is the distance between the body's center of mass (CM) and the suspension point. To set up the simple pendulum experiment, a student used a string of length l=1,4644 m and a spherical body of uniform density and radius l0=3,45 cm as suspended mass. a) Calculate the value of L from the suspension point to the center of mass (CM) of the body in this setup and write your result in meters to 4 decimal places. b)If the oscillation is done in small amplitudes, in which the MHS approximation is valid, what is the period of the oscillation? Give your answer to 4 decimal places.arrow_forward
- A group of astronauts, upon landing on planet X, performed a simple pendulum experiment in the MHS (Single Harmonic Movement, Small Amplitude) regime with length L=1,1132 m. In the experiment, the pendulum performs n=9 complete oscillations at t=13,5459 s. Calculate the gravity acceleration of planet X at the experiment location. Give your answer to 4 decimal places.arrow_forwardA scientist wishes to determine the acceleration of gravity on the surface of the planet Nos'Kere by experimenting with a pendulum. The length of the pendulum is 3.2 m, and the period of the pendulum is 2.3 s. unitarrow_forwardA 0.75 kg mass oscillates according to the equation x(t)=Acos(ωt). Here, A=0.67 m and ω=6.5 rad/s. What is the period, in seconds, of this mass?arrow_forward
- At an outdoor market, a bunch of bananasis set into oscillatory motion with an amplitude of 34.6313 cm on a spring with a springconstant of 14.7634 N/m. The mass of thebananas is 43.2987 kg.What is the maximum speed of the bananas?Answer in units of m/s.arrow_forwardA 0.75-kg mass oscillates according to the equation x(t)=0.85 cos(7.5t), where the position x(t) is measured in meters. What is the period, in seconds, of this mass? At what point during the cycle is the mass moving at its maximum speed?arrow_forwardThe motion of a body is described by the equation y = 2.70 sin(0.160πt), where t is in seconds and y is in meters. (a) Find the amplitude.(b) Find the angular frequency.(c) Find the period.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning