Vector a s is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. vector b s is 1.90 cm long and is 60.0° below th
e x-axis in the fourth quadrant (fig. e1.35). use components to find the magnitude and direction of (a) a s + b s ; (b) a s − b s ; (c) b s − a s . in each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.
Vector a is 2.8 cm long and 60° above the x-axis in the first quadrant. Therefore it s represented by
Vector b is 1.9 cm long and 60° below the x-axis in the fourth quadrant. Therefore it is represented by
The vectors may be written as a = 2.8*(cos60°, sin60°) = (1.445, 2.5028) b = 1.9*(cos60°, -sin60°) = (0.950, -1.6454)
Part (a) a + b = (1.445+0.950, 2.5028-1.6454) = (2.395, 0.8574) The magnitude of this vector is √[2.395² + 0.8574² ] = 2.5438 cm Its direction is tan⁻¹ (0.8574/2.395) = 19.7° above the x-axis, in the first quadrant. The resultant vector is shown in the figure below.
Part (b) Similarly obtain a - b = (0.495, 4.1485) The magnitude is 4.1777. The direction is 83° above the x-axis, in the 1st quadrant. The resultant vector is shown in the figure below.
Part (c) Similarly, obtain b - a = (-0.495, -4.1483) The magnitude is 4.1777. The direction is 83° below the negative x-axis, in the 3rd quadrant. The resultant vector is shown in the figure below.
The Earth rotates due to the manner in which it was formed. Earth began its rotation from the spinning movement of the accretion disk. In short, the earth rotates because of angular momentum caused by the accretion disk.
When it says something like 'on the verge of moving,' it means that the pulling force and static friction force and gravitational force all cancel out! Any more pulling force and it is ready to move!
At some point, you want F as a function of <span>μs</span>, to determine the force needed depending on the coefficient of static friction. This function, <span>F(<span>μs</span>)</span>, will rely on the angle θ as well, but we want to consider just one angle θ in every scenario. One value means it is constant.
But if we know the F, and we know <span>μs</span>, we can find what the constant angle θ must be!
If F is the pulling force, <span>FS</span> is the static friction force, and <span>FG</span> is gravitational force,
Then you can find <span>F(<span>μs</span>)</span>, but then there is the issue of solving for the θ<span> to make it true.</span>
Assuming your two trolleys stick together after the collision, your momentum equation would be M1V1+M2V2=(M1+M2)V3 and since V2 is 0, then 2x2=(2+2)V3, thereore the final velocity would be 1, wich would make the final momentum 4