Answer to Question #157318 in Mechanics | Relativity for Manisha Nayak

Question #157318

A crate of mass 40.0 kg is pulled by a force of 2000 N, up an inclined plane which 

makes an angle of 30º with the horizon. The coefficient of kinetic friction between the 

plane and the crate is miu.k = 0.20. If the crates starts from rest, calculate its speed after it 

has been pulled 10.0 m. Draw the free body diagram. Take 

g=10.0 ms-² .



1
Expert's answer
2021-01-21T16:13:47-0500

Let's draw a FBD:



Let's apply Newton's Second Law of Motion in projections on axis xx- and yy:


FpullmgsinθFfr=ma,F_{pull}-mgsin\theta-F_{fr}=ma,N=mgcosθ,N=mgcos\theta,Fpullmgsinθμkmgcosθ=ma.F_{pull}-mgsin\theta-\mu_k mgcos\theta=ma.

From this equation, we can find the acceleration of the crate:


a=Fpullmg(sinθ+μkcosθ)m,a=\dfrac{F_{pull}-mg(sin\theta+\mu_kcos\theta)}{m},a=2000 N40 kg10 ms2(sin30+0.2cos30)40 kg=43.3 ms2.a=\dfrac{2000\ N-40\ kg\cdot 10\ \dfrac{m}{s^2}\cdot(sin30^{\circ}+0.2\cdot cos30^{\circ})}{40\ kg}=43.3\ \dfrac{m}{s^2}.

Finally, we can find the speed of the crate after it has been pulled 10.0 m:


vf2=vi2+2ad,v_f^2=v_i^2+2ad,vf=2ad=243.3 ms210.0 m=29.43 ms.v_f=\sqrt{2ad}=\sqrt{2\cdot 43.3\ \dfrac{m}{s^2}\cdot10.0\ m}=29.43\ \dfrac{m}{s}.

Answer:

vf=29.43 ms.v_f=29.43\ \dfrac{m}{s}.


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