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Two packing crates of masses m1 = 10.0 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley. The 5.00 kg crate lies on a smooth incline of angle 36.0°. Find the acceleration of the 5.00 kg crate.
Been trying to figure this out. please show how you got the answer. your help is greatly appreciated!!!! Thanx!
***Also: Find the tension in the string.
3 Answers
- 1 decade agoFavorite Answer
the system is not in equilibrium and moves towards the side of the m1block. let there be tension t in the string and let the blocks move at acceleration a.
then for m1
m1g - t =m1 a ...................(1)
for m2
t -m2gsin36 = m2a ...............(2)
adding (1) &(2) and solving we get
a=4.6131866m/s sqr. towards direction of motion i.e.in direction m1 moving down which is also the acceleration of m2 .i.e 5kg block
subtiuting in any one of the eqns we get
t=51.86 N towards the opp. direction of motion
- Alexey VLv 51 decade ago
Forces on m1: m1*g and T, and according to 2nd law of motion: m1*a = m1*g - T, so T = m1*(g - a)
Forces on m2: m2*g downward, Fn - normal force perpendicular to incline, T along the incline. Resultant force is along the incline and according to 2nd law of motion equal to m2*a. Looking at components of forces parallel to incline we can write: m2*a = T - m2*g*sin(A), so T = m2*a + m2*g*sin(A) = m2*(a + g*sin(A)).
Now equate 2 expressions for T and get
m1*(g - a) = m2*(a + g*sin(A)).
m1*g - m2*g*sin(A) = m2*a + m1*a
a = (m1*g - m2*g*sin(A))/(m1 + m2)
To find T substitute a into T = m1*(g - a) and get
T = m1((m2*g + m2*g*sin(A))/(m1 + m2)) = m1*m2/(m1 + m2) *g(1 + sin(A))