How Do You Calculate the Total Force on a Block on an Inclined Plane?

[wrexsoul]

Newton's second law problem; Please Help!

Block M = 7.50 kg is initially moving up the incline and is increasing speed with
a = 4.35 m/s2. The applied force F is horizontal. The coefficients of friction
between the block and incline are fs = 0:443 and fk = 0:312. The angle of the incline is
25.0 degrees.
(a) What is the force F?

So basically, I started by tilting the axes. Then, I did F=ma. I plugged 7.5 kg into m and 4.35 into a. I got 32.6 N. Then, I took 32.6/cos(25) to get the horizontal component of force. My answer was 35.99 N. It says that my answer should be around 80 N to 120 N. What did I do wrong? Please Help.

 

[Doc Al]

To apply Newton's 2nd law you must consider all the forces. What other forces act parallel to the incline?

Hint: You'll need to analyze both vertical and horizontal force components.

 

[tomcue]

It seems like you have correctly applied Newton's second law, F=ma, to find the force F. However, it appears that you have only considered the horizontal component of the force, which is not the only force acting on the block. In this problem, there are two forces acting on the block: the applied force F and the force of friction between the block and the incline.

To find the total force acting on the block, you need to consider both the horizontal and vertical components. The vertical component of the force is due to the weight of the block, which can be calculated using the formula Fg=mg, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2). In this case, the vertical force is acting in the opposite direction of the applied force F.

To determine the value of F, you can set up an equation of forces in the vertical direction. The total vertical force acting on the block is equal to the sum of the vertical components of the applied force and the force of friction. So the equation would look like this:

Fg - Fsin(25) - fsN = 0

Where N is the normal force, which is equal to the weight of the block in this case. Solving for F, you should get a value between 80 N and 120 N, as indicated in the problem.

In summary, to find the force F, you need to consider both the horizontal and vertical components of the forces acting on the block. It is important to take into account all the forces in a problem involving Newton's second law. I hope this helps.