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Part C: Evaluate the numerical value of the final momentum of the t-shirt using the results from Parts A and B.

Part C: Evaluate the numerical value of the final momentum of the t-shirt using the results from Parts A and B.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter6: Momentum, Impulse, And Collisions
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Part C: Evaluate the numerical value of the final momentum of the t-shirt using the results from Parts A and B.

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 t = 0.5 s. The force as a function of time is given by F(t) = at² + b, 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=t¹ 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 = Submit ○ 0+(³+6) ○ 0+(½ t)|t¹ ○0+(³) 0+(gt3 +bt)l Previous Answers Correct We check that we have obtained the correct form of the integral by performing differentiation of t³ + bt with respect to t, which gives at² + b = F(t) as expected.
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 t = 0.5 s. The force as a function of time is given by F(t) = at² + b, 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=t¹ 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 = Submit ○ 0+(³+6) ○ 0+(½ t)|t¹ ○0+(³) 0+(gt3 +bt)l Previous Answers Correct We check that we have obtained the correct form of the integral by performing differentiation of t³ + bt with respect to t, which gives at² + b = F(t) as expected.
▼ Part B •t=t The units of the momentum of the t-shirt are the units of the integral St=t¹ F(t) dt, where F(t) has units of N and t has units of s. Given that 1 N = 1 kg. m/s², the units of momentum are: ► View Available Hint(s) kg. m/s kg/s kg • m/s³ kg. m/s² Submit Previous Answers Correct The units of a quantity obtained by integration will be the units of the integrand times the units of the differential.
Transcribed Image Text:▼ Part B •t=t The units of the momentum of the t-shirt are the units of the integral St=t¹ F(t) dt, where F(t) has units of N and t has units of s. Given that 1 N = 1 kg. m/s², the units of momentum are: ► View Available Hint(s) kg. m/s kg/s kg • m/s³ kg. m/s² Submit Previous Answers Correct The units of a quantity obtained by integration will be the units of the integrand times the units of the differential.
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