Question

8. While trying to move a piano across the room, Steve pushes on the piano with 150 N at

45° N of E and Ray pushes with 250 N 40° N of E. Bob and Ken both disagree with Steve
& Ray's plan, and begin pushing against them with 100 N 35° S of W and 400 N 45° S of
W, respectively. What is the overall resultant force on the piano? Solve using vector
resolution method.

Answer 1

The overall resultant force on the piano is (160 + 75sqrt(2)) N in the northward direction and (191.8 + 75sqrt(2)) N in the eastward direction.



Step-by-step explanation:
To find the overall resultant force on the piano, we need to first resolve the given forces into their north-south and east-west components.

For Steve's force of 150 N at 45° N of E, the north component is: 150 N * sin(45°) = 150 N * sqrt(2)/2 = 75sqrt(2) N

The east component is: 150 N * cos(45°) = 150 N * sqrt(2)/2 = 75sqrt(2) N

Similarly, for Ray's force of 250 N 40° N of E, the north component is: 250 N * sin(40°) = 250 N * sin(40°) = 160 N

The east component is: 250 N * cos(40°) = 250 N * cos(40°) = 191.8 N

Now, let's add up the north and south components separately and the east and west components separately.

Adding the north components: 75sqrt(2) N + 160 N = 75sqrt(2) N + 160 N = 160 + 75sqrt(2) N

Adding the east components: 75sqrt(2) N + 191.8 N = 75sqrt(2) N + 191.8 N = 191.8 N + 75sqrt(2) N

The overall resultant force on the piano is the sum of these two perpendicular components.

Therefore, the overall resultant force on the piano is (160 + 75sqrt(2)) N in the northward direction and (191.8 + 75sqrt(2)) N in the eastward direction.