Question

Un corp de masa m este tras cu accelerația a pe un plan orizontal de forță necunoscuta F care face unghiul alfa cu orizontala:
a)deasupra orizontalei
b)sub orizontala
Coeficientul de frecare corp-plan este miu.
m=50 kg;a=2,32m/s patrat; miu=0,268; unghiul alfa =30 grade

Answer 1

Presupun ca trebuie de aflat forta F, caci nimic nu ai scris :/
In orice caz, cel mai greu e sa aflii forta, pentru a afla alt ceva am folosit multe formule si deja gasesti ce iti trebuia.

Legile lui Newton (prima si a doua) se scriu pe axa Ox si Oy, orientinduse dupa desen, ai desenele la punctul a) si b) mai jos!



[tex]\displaystyle \text{a)Se da:}\\ \\ m=50kg\\ \\ a=2,32\frac{m}{s^2}\\ \\ \mu=0,268\\ \\ \alpha=30^\circ\\ \\ F=?N\\ \\ \\ \text{Formule:}\\ \\ \text{Pe axa O}_\text{y}\text{:}\\ \\ F_y+N-G=0\\ \\ F\times \sin\alpha+N-m\times g=0\\ \\ N=m\times g-F\times\sin\alpha\\ \\ \\[/tex]


[tex]\displaystyle \text{Pe axa O}_\text{x}\text{:}\\ \\ F_x-F_{fr}=m\times a\\ \\ F\times\cos\alpha-\mu\times N=m\times a\\ \\ F\times\cos\alpha-\mu\times(m\times g-F\times\sin\alpha)=m\times a\\ \\ F\times\cos\alpha-\mu\times m\times g+\mu\times F\times\sin\alpha=m\times a\\ \\ F\times\cos\alpha+\mu\times F\times\sin\alpha=m\times a+\mu\times m\times g\\ \\ F\times(\cos\alpha+\mu\times\sin\alpha)=m\times(a+\mu\times g)\\ \\ \\[/tex]


[tex]\displaystyle \boxed{F=\frac{m\times(a+\mu\times g)}{\cos\alpha+\mu\times\sin\alpha}}\\ \\ \\ \text{Calcule:}\\ \\ F=\frac{50\times(2,32+0,268\times 10)}{\cos30+0,268\times\sin30}\approx 250N[/tex]



[tex]\displaystyle \text{b)Se da:}\\ \\ m=50kg\\ \\ a=2,32\frac{m}{s^2}\\ \\ \mu=0,268\\ \\ \alpha=30^\circ\\ \\ F=?N\\ \\ \\ \text{Formule:}\\ \\ \text{Pe axa O}_\text{y}\text{:}\\ \\ N-G-F_y=0\\ \\ N-m\times g-F\times \sin\alpha=0\\ \\ N=m\times g+F\times\sin\alpha\\ \\ \\[/tex]


[tex]\displaystyle \text{Pe axa O}_\text{x}\text{:}\\ \\ F_x-F_{fr}=m\times a\\ \\ F\times\cos\alpha-\mu\times N=m\times a\\ \\ F\times\cos\alpha-\mu\times(m\times g+F\times\sin\alpha)=m\times a\\ \\ F\times\cos\alpha-\mu\times m\times g-\mu\times F\times\sin\alpha=m\times a\\ \\ F\times\cos\alpha-\mu\times F\times\sin\alpha=m\times a+\mu\times m\times g\\ \\ F\times(\cos\alpha-\mu\times\sin\alpha)=m\times(a+\mu\times g)\\ \\ \\[/tex]


[tex]\displaystyle \boxed{F=\frac{m\times(a+\mu\times g)}{\cos\alpha-\mu\times\sin\alpha}}\\ \\ \\ \text{Calcule:}\\ \\ F=\frac{50\times(2,32+0,268\times 10)}{\cos30-0,268\times\sin30}\approx 341,5N[/tex]