(2) Two forces $ F_1 = (36.0 \, \text{N})\mathbf{i} - (16.0 \, \text{N})\mathbf{j} $ and $ F_2(x, y) = (ax)\mathbf{i} + (by)\mathbf{j} $ displace a 12.0 kg object from the point $ (10.0 \, \text{m}, 10.0 \, \text{m}) $ to the point $ (30.0 \, \text{m}, 40.0 \, \text{m}) $. The numerical values of $ a $ and $ b $ are 6.0 and 8.0 respectively when the units of $ F_2(x, y) $ are Newtons.(a) What are the units of $ a $ and $ b $?(b) Calculate the work done on the object by the net force ($ F_{\text{net}} = F_1 + F_2 $) acting on it. (answer: 8640 J)(c) If the object started from rest at $ (10.0 \, \text{m}, 10.0 \, \text{m}) $, what was its speed when it reached $ (30.0 \, \text{m}, 40.0 \, \text{m}) $? (answer: 37.9 m/s)

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Answered: (2) Two forces F₁ = (36.0 N)i - (16.0…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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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(2) Two forces $ F_1 = (36.0 \, \text{N})\mathbf{i} - (16.0 \, \text{N})\mathbf{j} $ and $ F_2(x, y) = (ax)\mathbf{i} + (by)\mathbf{j} $ displace a 12.0 kg object from the point $ (10.0 \, \text{m}, 10.0 \, \text{m}) $ to the point $ (30.0 \, \text{m}, 40.0 \, \text{m}) $. The numerical values of $ a $ and $ b $ are 6.0 and 8.0 respectively when the units of $ F_2(x, y) $ are Newtons.

(a) What are the units of $ a $ and $ b $?

(b) Calculate the work done on the object by the net force ($ F_{\text{net}} = F_1 + F_2 $) acting on it. (answer: 8640 J)

(c) If the object started from rest at $ (10.0 \, \text{m}, 10.0 \, \text{m}) $, what was its speed when it reached $ (30.0 \, \text{m}, 40.0 \, \text{m}) $? (answer: 37.9 m/s)

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$text Forces: end text stack F subscript 1 with rightwards arrow on top equals 36 i minus 16 j stack F subscript 2 with rightwards arrow on top equals a x i plus b y j space space space space space space space space space space space space space space space space space space space space left parenthesis a equals 6 comma space b equals 8 right parenthesis text Mass of object: end text m equals 12 space k g text Initial position: end text stack r subscript i with rightwards arrow on top equals left parenthesis 10 m comma space 10 space m right parenthesis text Final position: end text stack r subscript f with rightwards arrow on top equals left parenthesis 30 m comma space 40 space m right parenthesis$

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