Friction Question an incline plane with two angles

[SS_KingTiger]

Ok I just can't see this questions I don't want an answer I just whant an explation on how to do it. if you can respond today it would be great thanks! an simple drawing like I did would be great thanks!

a block weighing 100 Newtons is positioned on a incline that makes an angle of 30 degrees with the horizontal. The friction force between the block and the incline is 10 Newtons. A force of 120 Newtons is applied by pulling on a rope that makes an angle of 30 degrees with the incline as shown in attachment.

1. Determine the components of the block's weight parallel to incline (is that Fg?)

2. Determine the magnitude and direction of the componet of the tension that is useful in moving the block up the incline. (tension)

3. Determine the magnitude and direction of the block acceleration.

 

[daniel_i_l]

For 1 and 2:
set up the coordinate system so that the x-axis is parallel to the incline.
for 1 find the angle between the x-axis and the weight (gravitational force) of the block. Then multiply by cos(angle). Same for 2.
For 3, find the sum of the forces on the x-axis and the y-axis. Then use F=ma.

 

[quicknote]

Hello,

Thank you for your question. I am happy to provide an explanation on how to approach this problem.

First, it is important to understand that friction is a force that opposes motion between two surfaces in contact. In this scenario, the block is on an incline plane, meaning it is at an angle relative to the horizontal surface. The angle of the incline plane will affect the components of the block's weight and the direction of the tension force.

To begin, let's label the forces acting on the block. The block's weight, also known as its force of gravity (Fg), is always directed downwards towards the center of the Earth. In this case, the weight is 100 Newtons. However, since the block is on an incline plane, we need to determine the components of the weight that are parallel and perpendicular to the incline.

To determine the component of the weight parallel to the incline, we need to use trigonometry. The angle between the weight and the incline is 30 degrees, so we can use the formula Fpar = Fg * sin(30) = 100 * sin(30) = 50 Newtons. This means that 50 Newtons of the block's weight is acting parallel to the incline.

Next, we need to determine the tension force. The tension force is the force applied by pulling on the rope, and it is directed along the rope's length. In this case, the rope makes an angle of 30 degrees with the incline, so we can use the same formula as before to determine the component of the tension force that is parallel to the incline. Fpar = Ft * sin(30) = 120 * sin(30) = 60 Newtons. This means that 60 Newtons of the tension force is acting parallel to the incline and is useful in moving the block up the incline.

Finally, we can determine the magnitude and direction of the block's acceleration. To do this, we can use Newton's Second Law, which states that the net force acting on an object is equal to its mass times its acceleration (Fnet = ma). In this case, the net force is the sum of the parallel forces acting on the block, so we can write the equation as Fpar = ma. We know the values for the parallel forces (50N and 60N) and the mass of the block (100N), so we