There are many well-documented cases of people surviving falls from heights greater than 20.0 m. In one such case, a 55.0 kg woman survived a fall from a 10th floor balcony, 29.0 m above the ground, onto the garden below, where the soil had been turned in preparation for planting.Because of the "give" in the soil, which the woman compressed a distance of 15.0 cm upon impact, she survived the fall and was only briefly hospitalized.(a) Ignoring air resistance, what was her impact speed with the ground (in m/s)?m/s(b) What was the magnitude of her deceleration during the impact in terms of g?g(c) Assuming a constant acceleration, what was the time interval (in s) during which the soil brought her to a stop?S(d) What was the magnitude of the impulse (in N⚫ s) felt by the woman during impact?N⚫s(e) What was the magnitude of the average force (in N) felt by the woman during impact?N

Answered: There are many well-documented cases of…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter9: Energy In Nonisolated Systems

Section: Chapter Questions

Problem 1PQ: Pick an isolated system for the following scenarios while including the fewest number of objects as...

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An athlete jumping vertically on a trampoline leaves the surface with a velocity of 8.5 m/s upward. What maximum height does she reach? (a) 13 m (b) 2.3 m (c) 3.7 m (d) 0.27 m (e) The answer cant be determined because the mass of the athlete isnt given.
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.
A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively, (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data, (b) Determine the acceleration of the cart from the slope of this graph, (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 5.6.
Neglecting air resistance, how much would I have to raise the vertical height if I wanted to double the impact speed of a falling object?
For t 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet=mkv2i, where k is a constant. The speed of the object after t = 0 is given by v = vi/(1 + kvit). (a) Find the position x of the object as a function of time. (b) Find the objects velocity as a function of position.
To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam around the house(Fig. P13.66). When a hamsteris in such a ball, it can cross atypical room in a few minutes.Estimate the total kinetic energyin the ball-hamster system. FIGURE P13.66 Problems 66 and 67
A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 0 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the hall have maximum speed? (c) What is this maximum speed?
A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.68a). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring (Fig. P7.68b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Fig. P7.68c). The object is then forced toward the left by the spring (Fig. P7.68d) and continues to move in that direction beyond the springs unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Fig. P7.68e). Find (a) the distance of compression d, (b) the speed v at the unstretched position when the object is moving to the left (Fig. P7.68d), and (c) the distance D where the object comes to rest. Figure P7.68
The speed of a particle of mass m varies with the distance x as υ(x) = αx−n. Assume υ(x = 0) = 0 at t = 0. (a) Find the force F(x) responsible. (b) Determine x(t) and (c) F(t).
A particle moves in a medium under the influence of a retarding force equal to mk(υ3+ a2υ), where k and a are constants. Show that for any value of the initial speed the particle will never move a distance greater than π/2kaand that the particle comes to rest only for t → ∞.
Why is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The ball launcher in the machine sends metal balls up one side of the machine and then into play. The spring in the launcher (Fig. P6.60) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting.

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