Block 1 (10 kg) is pulled by a rope from left to right up a ramp which is inclin

Question

Block 1 (10 kg) is pulled by a rope from left to right up a ramp which is inclined 25 degrees from the horizontal. The rope pulls on block 1 with a force of 190 N parallel to the surface of the inclined plane. The coefficient of kinetic friction between the block and the surface equals 0.6. On a sheet of paper, draw the free body diagram for block 1 using the two-subscript notation from class. Assume that the x-axis is parallel to the incline and positive in the direction up the incline. After completing the free body diagram, enter below each force and its x & y-components.

FORCES on BLOCK 1

Weight force on block 1 by Earth

W1E = i + j N

Tension force on block 1 by Rope

T1R = i + j N

Normal force on block 1 by Surface

N1S = i + j N

Frictional force on block 1 by Surface

f1S = i + j N

What is the acceleration a of block 1?

a = i + j m/s2

Explanation / Answer

Here,
uk = 0.6

A)
Weight force on block :
W = mgSin25 i + mgCos25 j
W = mg(Sin25i + Cos25j)
W = 98(0.42 i + 0.90 j)
W = ( 41.16 i + 88.2 j ) N

B)
Tension in Rope can be found out by using Newton Second law Fnet =0

Tx - Wx -Ff = 0
Tx - Wx - ukWy = 0
Tx = Wx -uk*Wy
Tx = 41.16 - 0.6*88.2
Tx = 35.868 N i

As motion is along horizonatal
Ty = 0 j

T = (35.868 i + 0 j) N

C)
As normal Force always act perpendicular to surface or motion Terefore
N = (0 i + Wy j)
N = (0 i + 88.2 j) N

D)

Frictional Force always act opposite to directin of motion :
Ffx = uk * 88.2 i
Ffx = 0.6*88.2 i
Ff = (52.92i + 0 j) N

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