Question
The three forces shown in Figure $\mathrm{P} 4.2$ act on a particle. If the particle is in translational equilibrium, find $F_{3}$ (the magnitude of force 3 ) and the angle $\theta_{3}$.
Step 1
We can do this using the cosine of the given angles. For $F_1$, we have $F_{1x} = F_1 \cos(60^\circ) = 15 \cos(60^\circ) = 7.5$ N. For $F_2$, we have $F_{2x} = F_2 \cos(30^\circ) = 24 \cos(30^\circ) = 20.78$ N. Show more…
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Several forces act on a particle as shown in Figure $\mathrm{P} 4.3 .$ If the particle is in translational equilibrium, what are the values of $F_{3}$ (the magnitude of force 3 ) and $\theta_{3}$ (the angle that force 3 makes with the $x$ axis)?
Forces and Motion in Two and Three Dimensions
Statics
A particle is acted on by forces given, in newtons, by $\vec{F}_{1}=$ $8.40 \hat{\mathrm{i}}-5.70 \hat{\mathrm{j}}$ and $\vec{F}_{2}=16.0 \hat{\mathrm{i}}+4.10 \hat{\mathrm{j}}$ . (a) What are the $x$ component and (b) $y$ component of the force $\vec{F}_{3}$ that balances the sum of these forces? (c) What angle does $\vec{F}_{3}$ have relative to the $+x$ axis?
A particle is acted on by forces given, in newtons, by $\vec{F}_{1}=$ $8.40 i-5.70 j$ and $\vec{F}_{2}=16.0 i+4.10 j_{4}$, (a) What are the $x$ component and (b) $y$ component of the force $\vec{F}_{3}$ that balances the sum of these forces? (c) What angle does $\vec{F}_{3}$ have relative to the $+x$ axis?
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