Physics
posted by Andrew on .
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.

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:
FnmgFsin(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!