Question

1.Four forces - 11 N oriented in positive x- axis, 10.3 N oriented at 60 degrees with positive x- axis, 7 N oriented in negative y- axis, and 2.1 N oriiented at 135 degrees with positive x- axis, are working on 6.9 kg object. What is the acceleration?

2.Two blocks of masses m1 =2 kg and m2 = 2 kg are connected by a string. One block (m1) slides on a table and the other (m2) hangs from the string, which passes over a pulley. The coefficient of kinetic friction is 0.20. What is acceleration of the blocks?

Answer 1

Here ,

force , F1 = 11 i N

F2 = 10.3 * (cos(60) i + j * sin(60)) = 5.15 i + 8.92 j N

F3 = -7 j N

F4 = 2.1 *(cos(135) i + j * sin(135))

Now , net force is Fnet = F1 + F2 + F3 + F4

Using second law of motion

m * a = 11 i + 5.15 i + 8.92 j -7 j 2.1 *(cos(135) i + j * sin(135))

6.9 * a = 11 i + 5.15 i + 8.92 j -7 j + 2.1 *(cos(135) i + j * sin(135))

a = ( 14.7 i + 3.41 j )/6.9

a = 2.13 i + 0.493 j m/s^2 = sqrt(2.13^2 + 0.493^2 ) at arctan(0.493/2.13) degree

the acceleration is 2.19 m/s^2 at 13.03 degree