Angle Between F1 and F2 Forces on Disk Sliding on Ice

[KMjuniormint5]

The question is:

Two horizontal forces F1 and F2 act on a 1.8 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force F1 is in the negative direction of the x-axis and has a magnitude of 3.0 N. Force F2 has a magnitude of 9.0 N. The figure below gives the x component vx of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces F1 and F2?

The graph is a Vs(m/s) vs t(s). It starts down at -4 m/s when time = 0 and it is a staight line up to +5m/s at time = 3 and the function crossed the x-axis around 1.3333ish (doesnt give an exact point).

how do I go about interupting this graph to help give me F2net . . .I think i know how to get the angle and I know that . . .

F1x = 3.0 N and F1y = 0 N so. . how to get F2x and F2y from the graph. .

 

[nnyms]

Hint to Sliding Forces Problem

Let's list all given data.
- 1.8 kg disk
- F1 = -3.0 N (because it go in negative direction)
- F2 = 9.0 N (but we don't know which direction it go)
- a = ? (it will be slope of your graph because your graph show velocity and if you derivative the velocity then you will get acceleration)

Use Newton's Second Law, Force = Mass x Acceleration.
The Force will be sum of F1 and F2. The Mass will be mass of disk. The Acceleration will be the slope of your velocity graph.

You will need to find F2x. (Note: the graph will not help you to find it.) Use cosine. The answer for F2x will be F2x = 9.0cos(d)

Set up an equation.
F1 + F2 = M x A
-3.0N + 9.0cos(d)N = 1.8kg x A

Go ahead find acceleration, then solve for angle 'd'. Let me know if you need any more hint and help.

 

[Moetasim]

From the graph, it can be seen that the velocity of the disk increases from -4 m/s to +5 m/s in a linear fashion over the course of 3 seconds. This means that the acceleration of the disk is constant and the net force acting on the disk is also constant. In order to determine the angle between F1 and F2, we can use the formula for the magnitude of the net force, which is equal to the mass of the object multiplied by its acceleration (Fnet = ma). In this case, the mass of the disk is given as 1.8 kg and the acceleration can be calculated from the slope of the velocity vs time graph, which is equal to (5-(-4))/3 = 3 m/s^2. Therefore, the net force acting on the disk is 1.8 kg * 3 m/s^2 = 5.4 N.

Next, we can use trigonometry to determine the individual components of F2 (F2x and F2y) based on the angle between F1 and F2. The angle can be found using the inverse tangent function (tan^-1) of the slope of the velocity vs time graph, which is equal to 3 m/s^2. This gives us an angle of approximately 71.6 degrees.

Using this angle, we can calculate the individual components of F2 using the formula F2x = F2 * cosθ and F2y = F2 * sinθ, where θ is the angle between F1 and F2. Plugging in the values, we get F2x = 9 N * cos(71.6 degrees) = 3.0 N and F2y = 9 N * sin(71.6 degrees) = 8.3 N.

Therefore, the angle between F1 and F2 is approximately 71.6 degrees and the components of F2 are F2x = 3.0 N and F2y = 8.3 N.