What is the upper block\'s acceleration if the coefficient of kinetic friction b

Question

What is the upper block's acceleration if the coefficient of kinetic friction between the block and the table is 0.28?

What I know:

F=ma

Fk = uk(n)

n = mg

Box 1: F(net) = m1*a = T - uk(m1*g)

Box 2: F(net) = m2*a = T - m2*g

Since I have two unknowns, I set the first equation equal to T

Box 1: T = uk(m1*g) + m1*a

Box 2: T - m2g = m2*a

I substitututed the T into the Box 2 equation and got

uk(m1*g) + m1*a - m2*g = m2*a

When I solved for 'a', I subtracted (m1*a) from both sides and obtained:

uk(m1*g) - m2*g = m2*a - m1*a

it simplified to

uk(m1*g) - m2*g = (m2 - m1) a

divide (m2-m1) from both sides

a = uk(m1*g) - m2*g / (m2-m1) my formula (wrong)

a = uk(m1*g) - m2*g / (m2+m1) correct formula

You're suppose to ADD (m2+m1) to recieve the correct answer and I dont understand why?

Some people solved it with Box 1: formula being ma = uk(m1*g) - T

I dont understand, shouldnt the friction force be negative? Not T

PLEASE help me understand how they're adding (m1+m2) and not subtracting. My exam is tomorrow :-(

What is the upper block's acceleration if the coefficient of kinetic friction between the block and the table is 0.28? What I know: F=ma Fk = uk(n) n = mg Box 1: F(net) = m1*a = T - uk(m1*g) Box 2: F(net) = m2*a = T - m2*g Since I have two unknowns, I set the first equation equal to T Box 1: T = uk(m1*g) + m1*a Box 2: T - m2g = m2*a I substitututed the T into the Box 2 equation and got uk(m1*g) + m1*a - m2*g = m2*a When I solved for 'a', I subtracted (m1*a) from both sides and obtained: uk(m1*g) - m2*g = m2*a - m1*a it simplified to uk(m1*g) - m2*g = (m2 - m1) a divide (m2-m1) from both sides a = uk(m1*g) - m2*g / (m2-m1) my formula (wrong) a = uk(m1*g) - m2*g / (m2+m1) correct formula You're suppose to ADD (m2+m1) to recieve the correct answer and I dont understand why? Some people solved it with Box 1: formula being ma = uk(m1*g) - T I dont understand, shouldnt the friction force be negative? Not T PLEASE help me understand how they're adding (m1+m2) and not subtracting. My exam is tomorrow :-(

Explanation / Answer

for box2,

Box 2: T - m2g = m2*a

is wrong

m2g - T = m2a is correct.

m2g > T and acceleration is downwards. correct it.

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