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Nelonski
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Homework Statement
Determine the acceleration of a 10kg block traveling up a ramp connected by a massless string and massless pulley to another block that is 5kg and in free-fall. if the coefficient of kinetic friction between the block and the ramp is 0.2
(The diagram shows one block that is 10kg traveling up a slope at 40 degrees, and a second block falling with a rope connected to it upwards)
Homework Equations
Newtons 2nd law
f_x = Newtons law in x direction
f_y= Newtons law in y direction
T= tension force
f_k = friction force
n= normal force
w_1 = weight of block 1 (ramp)
w_2= weight of block 2(ramp)
The Attempt at a Solution
FBD_1 : The FBD of the block going up the ramp has axis tilted so that the normal force is in the positive y direction, kinetic friction to the negative x direction, tension to the positive x direction, and weight which has two components to it pointing down.
FBD_2: The second block in free-fall has tension upwards since it is connected by a string and its weight downwards
Block on ramp: F_x= -f_k +T + w_1sin∅=ma (1)
F_y= n-w_1cos∅ (2)
Frictional force can be solved for by solving for normal force, then subbing into μkn.
The acceleration in block 1 and block two are the same with massless/frictionaless pulley and string approximation.
Block in free fall: F_y=T-w_2=m_2a (3)
... The only unknown is the tension and the acceleration. So, I solved for the acceleration in
block 2 and subbed it into equation 1 to solve the tension. Then plugged the tension force into equation 1 again and solved for the acceleration..
Essentially, subbed equation 3 into equation 1, then plugged the tension value into eq 1 and solved for acceleration, which came out to be around 20 . seemed kind of high to me .
would those steps be considered right?