Question

This is for physics class.

Sally applies 32 N of force at an angle of 22 degrees above the horizontal to a 12 kg crate.

Ignoring friction, calculate the horizontal acceleration of the crate?

Conceptual: will the acceleration of the crate increase or decrease if the same force is applied at an angle of 16 degrees? Explain.

Answer 1

Start with a picture if you don't already have one and then draw a free body diagram (a dot with arrows to represent all the forces applied to the box if you don't know what that is go ahead and google it- it'll make sense if you see a picture). We can assume up and the direction of the applied force (F) is positive.
Forces in the y direction:
+Fn (normal force)
-mg (mass*gravity)
-F*sin(theta)

Fsin(theta) is the componet of the applied force in the y direction. If you remember the trig identites sin(theta)=opposite/hypotenuse. Here, the applied force is the hypo. so you get Fsin(theta)= the y component of the applied force since it is ppposite the angle at which the force is applied to the box.

X direction:
+Fcos(theta)

This is the same as the y component of the applied force except its the adjacent side to the angle and acts in the x direction.

Ok if that all made sense (I hope it did) now you're ready to write two equations, one in the x direction and one in the y, based on Newton's second law F=ma

Y direction:
Fn-mg-Fsin(theta)=ma

X direction:
Fcos(theta)=ma

Since you have all the information in the x direction substitute with numbers and solve for a. It should come out to be something around 2.47 m/s^2 if you rounded the same way I did.

PS if there was friction you would subtract its force from the x direction when using sum of forces = ma.

Hope this helps!