What is force if acceleration is .75? (inclined plane)

[skysunsand]

Homework Statement

A horizontal force F is exerted on a 20kg box to slide it up a 30 degree incline. The friction force retarding the motion is 80N. How large must F be if the acceleration of the moving box is to be .75 m/s^2?

Homework Equations

All the forces on the box in the x and y direction have to equal zero

F=ma
F-Ff-Fn = ma

The Attempt at a Solution

Using F-Ff-Fn,

F-80-20*9.8*sin(30) = 20*.75
F-178= 15
F= 193 N

Which isn't even close to what the answer is supposed to be, which is F=220 N

 

[gneill]

If the box is accelerating then there must be a net force. Newton's first law.

 

[skysunsand]

If the box is accelerating then there must be a net force. Newton's first law.

How does that change my equations?

 

[gneill]

How does that change my equations?

Draw a Free Body Diagram for the box. There must be a net force that produces an acceleration of 0.75m/s² (acting up-slope). So what forces act along the slope?

 

[asteriatic]

.

I would like to point out that force is a vector quantity that is defined as any influence that causes an object to undergo a change in motion. In this case, the force F is the horizontal force that is being applied to the box to move it up the inclined plane. The acceleration of the box is 0.75 m/s^2, which means that for every second that passes, the velocity of the box will increase by 0.75 m/s.

In order to find the magnitude of force required to achieve this acceleration, we can use the equation F=ma, where m is the mass of the box and a is the acceleration. Plugging in the given values, we get F=20*0.75= 15 N. However, this is not the correct answer.

The reason for the discrepancy is due to the presence of friction. The friction force, Ff, acts in the opposite direction of the motion and retards the movement of the box. In this case, Ff is equal to 80 N. Therefore, the net force acting on the box is not just F, but it is F-Ff.

To find the magnitude of force required to achieve the given acceleration, we can use the equation F-Ff=ma. Substituting the values, we get F-80 = 20*0.75, which gives us F= 20*0.75+80= 95 N. However, this is still not the correct answer.

The reason for this is because the force F is acting at an angle of 30 degrees to the horizontal, while the acceleration is in the horizontal direction. Therefore, we need to resolve the force F into its components along the x and y axis.

Using trigonometry, we can find that the x component of F is equal to F*cos(30) and the y component is equal to F*sin(30). Since we are only concerned with the x component, we can rewrite the equation as F*cos(30)-80= 20*0.75. Solving for F, we get F= (20*0.75+80)/cos(30)= 220 N. This is the correct answer.

In conclusion, force is the cause of acceleration and in order to achieve a specific acceleration on an object, we need to consider all the forces acting on it, including friction and the direction of the applied force.