Help finding the magnitude of the applied force

[ssh222]

Homework Statement

A block of mass 50 kg is free to slide on a frictionless inclined plane that makes an angle of 20° with respect to horizontal. A force F is applied as shown in the drawing pulling parallel to the incline. As a result, the block accelerates up the plane at 4 m/s2.

known:
m= 50 kg
a= 4 m/s^2
Angle = 20 degrees

Homework Equations

F=ma
Fcos(theta)

The Attempt at a Solution

F= 50kg* 4m/s2 = 200 N
200cos(20)=187.9= F x-direction

* The explanation shows me F- 167 N = 200N
F=367N
But I don't know which equation this comes from or where the 167 comes from.

 

[azizlwl]

3. The Attempt at a Solution
F= 50kg* 4m/s2 = 200 N
200cos(20)=187.9= F x-direction
......
200cos(20)=187.9= F x-direction
What force is this?

 

[ssh222]

This was my attempt at finding the applied force..

 

[azizlwl]

Can you tell me why you multiply 200 with Cos(20)?

If you just put an object on frictionless inclined plane, in which direction the object moves?. What makes it move in that direction?

 

[Nickie]

I would first commend the student for attempting to solve the problem and using the correct equations. However, I would point out that the value of 167 N in the explanation is incorrect. The correct value for the applied force F is indeed 200 N, as calculated correctly by the student.

The confusion may arise from the use of the cosine function in the equation Fcos(theta). This equation is used to find the component of the force in the direction of the incline, not the total force. In this case, the component of the force in the x-direction is equal to the total force, since the incline is at an angle of 20 degrees with respect to the horizontal. Therefore, the correct equation to use is F=ma, where F is the total force and m is the mass of the block.

As for the 167 N mentioned in the explanation, it is not clear where this value comes from. It is possible that it was a mistake or a typo. As a scientist, it is important to double check all calculations and make sure they are accurate. In this case, the correct value of 200 N was calculated, and there is no need for further explanation or equations.