Four forces act on a hot-air balloon, shown from the side in the figure below. Find the magnitude and direction of the resultant force on the balloon if F1 = 4750 N, F2 = 1300 N, F3 = 950 N, and F4 = 3600 N.
_____ N at _______° clockwise from F2
To find the magnitude and direction of the resultant force on the balloon, we can use vector addition. The resultant force is the sum of all the individual forces acting on the balloon.
First, let's find the horizontal and vertical components of each force:
F1: Since it is not given in which direction F1 is acting, we will assume it acts horizontally. Therefore, the horizontal component of F1 is 4750 N and the vertical component is 0 N.
F2: It is given as 1300 N, and since it is not stated whether it acts horizontally or vertically, we will assume it acts vertically. Therefore, the horizontal component of F2 is 0 N and the vertical component is 1300 N.
F3: It is given as 950 N, and since it is not stated whether it acts horizontally or vertically, we will assume it acts vertically. Therefore, the horizontal component of F3 is 0 N and the vertical component is 950 N.
F4: It is given as 3600 N, and since it is not stated whether it acts horizontally or vertically, we will assume it acts vertically. Therefore, the horizontal component of F4 is 0 N and the vertical component is 3600 N.
Now, let's add up all the horizontal and vertical components to find the resultant force:
Horizontal component: 4750 N + 0 N + 0 N + 0 N = 4750 N
Vertical component: 0 N + 1300 N + 950 N + 3600 N = 5850 N
To find the magnitude of the resultant force, we can use the Pythagorean theorem:
Resultant force magnitude = sqrt((horizontal component)^2 + (vertical component)^2)
= sqrt((4750 N)^2 + (5850 N)^2)
= sqrt(22,562,500 N^2 + 34,222,500 N^2)
= sqrt(56,785,000 N^2)
≈ 7532.76 N
To find the direction of the resultant force, we can use trigonometry. We can use the inverse tangent function to find the angle:
Resultant force angle = atan(vertical component / horizontal component)
= atan(5850 N / 4750 N)
= atan(1.23)
≈ 51.06°
So, the magnitude of the resultant force on the balloon is approximately 7532.76 N, and it is at an angle of approximately 51.06° clockwise from the vertical force F2.