Part A The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of t₁ = 0.5 s. The force as a function of time is given by F(t) = at2b, where a = − -28 N/s² and b = 7.0 N. t=tL The momentum of the t-shirt will be its initial momentum (po = 0) plus its change in momentum due to the applied impulse: pf = po+ St= F(t) dt. By applying the given time dependent function for F (t) and performing the integration, which of the following is the correct expression for Pf? ▸ View Available Hint(s) Pf 0+(3+b) L ○ 0+ (11³) 160/20 ○ 0+ (1 +³ + bt) | 100 L ○ 0+ (12+) 10/20

College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Part A
The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball
games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of t₁ = 0.5 s. The force as a function of time is given by
F(t) = at2b, where a = −
-28 N/s² and b = 7.0 N.
t=tL
The momentum of the t-shirt will be its initial momentum (po = 0) plus its change in momentum due to the applied impulse: pf = po+ St= F(t) dt. By applying the given time dependent function for F (t) and performing the integration, which of the following is the correct expression for
Pf?
▸ View Available Hint(s)
Pf
0+(3+b)
L
○ 0+ (11³) 160/20
○ 0+ (1 +³ + bt) | 100
L
○ 0+ (12+) 10/20
Transcribed Image Text:Part A The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of t₁ = 0.5 s. The force as a function of time is given by F(t) = at2b, where a = − -28 N/s² and b = 7.0 N. t=tL The momentum of the t-shirt will be its initial momentum (po = 0) plus its change in momentum due to the applied impulse: pf = po+ St= F(t) dt. By applying the given time dependent function for F (t) and performing the integration, which of the following is the correct expression for Pf? ▸ View Available Hint(s) Pf 0+(3+b) L ○ 0+ (11³) 160/20 ○ 0+ (1 +³ + bt) | 100 L ○ 0+ (12+) 10/20
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