The integral with respect to time of a force applied to an object is a measure...
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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. The momentum of the t-shirt will be its initial momentum (p = 0) plus its change in momentum due to the applied impulse: p = 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 pj? +(을)기함 Ⓒ0+(3³+b) Pf= 0+(³+b) 0+(³) t=ti The units of the momentum of the t-shirt are the units of the integral ft 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: kg. m/s³ kg. m/s kg/s kg. m/s² Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010J (where 1 J = 1 N. m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE₂-KE₁ = F(x) dr. The net force exerted by the tractor beam is supposed to be constant, F = -3.5 x 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position is given by F(x) = ax³ + ẞ, where a = 6.1 × 10 9 N/m³ and 8=-4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 x 104 m away.from its beginning position at x = 0.0m. Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ +8.. 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. The momentum of the t-shirt will be its initial momentum (p = 0) plus its change in momentum due to the applied impulse: p = 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 pj? +(을)기함 Ⓒ0+(3³+b) Pf= 0+(³+b) 0+(³) 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. The momentum of the t-shirt will be its initial momentum (p = 0) plus its change in momentum due to the applied impulse: p = 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 pj? +(을)기함 Ⓒ0+(3³+b) Pf= 0+(³+b) 0+(³) t=ti The units of the momentum of the t-shirt are the units of the integral ft 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: kg. m/s³ kg. m/s kg/s kg. m/s² t=ti The units of the momentum of the t-shirt are the units of the integral ft 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: kg. m/s³ kg. m/s kg/s kg. m/s² Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010J (where 1 J = 1 N. m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE₂-KE₁ = F(x) dr. The net force exerted by the tractor beam is supposed to be constant, F = -3.5 x 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position is given by F(x) = ax³ + ẞ, where a = 6.1 × 10 9 N/m³ and 8=-4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 x 104 m away.from its beginning position at x = 0.0m. Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010J (where 1 J = 1 N. m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE₂-KE₁ = F(x) dr. The net force exerted by the tractor beam is supposed to be constant, F = -3.5 x 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position is given by F(x) = ax³ + ẞ, where a = 6.1 × 10 9 N/m³ and 8=-4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 x 104 m away.from its beginning position at x = 0.0m. Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ +8.. Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ +8..
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Managerial Decision Modeling With Spreadsheets
ISBN: 9780136115830
3rd Edition
Authors: Nagraj Balakrishnan, Barry Render, Jr. Ralph M. Stair
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