Two horizontal forces F1 and F2 act on a 1.7 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. What is the angle between the constant directions of forces F1 and F2?

i hate physics omfg

Based on the velocity vs time graph we can create a slope and equation of the line. The slope is y2-y1/x2-x1 or (5+4)/(3-0). This gives us a slope of 3. The y intercept of the V vs T graph is -4 so our Vx equation is 3t-4. The derivative of this equation is 3m/s^2 which gives us the x component of acceleration. Using the formula ∑F=ma we try to find the sum of the forces in the x direction. We already know one of the forces (F1) is 7N in the x direction since it is given. We now need to find the other one based off of F2. To find the x component we take 9cosӨ=F2x. Now we plug these into the formula ∑F=ma and get 7+9cosӨ=4kg•3 where 4 is our mass and 3 is our x component of acceleration. Using algebra you get theta to be 56.25 degrees.

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what is the formula??? or proceedure?? ty :)

Correction to my previous post, substitute 4kg for 1.7 kg and flip the x values to the negative since they are pointing in the negative x direction. It is still the same concept though.

Why did the disk go to therapy? Because it couldn't find its "angle of direction"!

But fear not! I'm here to help. To find the angle between the constant directions of forces F1 and F2, we can use some trigonometry. The resulting angle can be found using the formula tan(theta) = (F2 sin(alpha)) / (F1 + F2 cos(alpha)), where alpha is the angle we're looking for.

Plugging in the values, we have tan(theta) = (9.0 N * sin(alpha)) / (3.0 N + 9.0 N * cos(alpha)). From there, we can solve for the angle by substituting different values for alpha and finding which one makes the equation true. Good luck!

To find the angle between the constant directions of forces F1 and F2, we'll use the concept of vector addition.

First, let's represent the forces as vectors. Since F1 is in the negative direction of the x-axis, we can write F1 as (-3.0 N, 0). F2 can be represented as (0 N, 9.0 N) since it acts along the y-axis.

Next, we'll find the resultant vector F, which represents the combination of F1 and F2. To do this, we'll use the Pythagorean theorem and trigonometric functions. The magnitude of F is given by the square root of the sum of the squares of the x and y components:

|F| = sqrt((-3.0 N)^2 + (9.0 N)^2)
= sqrt(9.0 N^2 + 81.0 N^2)
= sqrt(90.0 N^2)
= 9.49 N

To find the angle between F1 and F2, we'll use trigonometric functions. The angle can be determined using the equation:

tan(θ) = (F2y/F1x)

Here, F2y represents the y-component of F2, and F1x represents the x-component of F1.

F2y = 9.0 N
F1x = -3.0 N

Therefore, tan(θ) = (9.0 N)/(-3.0 N) = -3.0

Now, we can find the angle θ by taking the inverse tangent of -3.0:

θ = tan^(-1)(-3.0)
= -71.57°

Since the angle is negative, we can add 180° to get the positive angle:

θ = -71.57° + 180°
= 108.43°

Therefore, the angle between the constant directions of forces F1 and F2 is approximately 108.43°.