Could anyone help me set up this equation? I drew my force body diagram but wasn't sure how to include the downward force (im assuming i use either sine or cosine?)
A force of 340 N pushes a 54 kg object. Find the acceleration of the box if the force makes an angle of 70 degrees from the vertical (the force is pushing down on the box). The coefficient of kinetic friction is 0.4.
Fap = 340 N.[20o] Above the hor.
Mass = 54 kg.
u(k) = 0.4
m*g = 54 * 9.8 = 529.2 N. = Wt. of object.
Fn = m*g+Fap*sin20=529.2 N. + 340*Sin20 = 645.5 N. = Normal = Force perpendicular to the surface.
Fk = u*Fn = 0.4 * 645.5 = 258.2 N.
a = (Fap*Cos20-Fk)/m = (319.5-258.2)/54=
1.14 m/s.
Fn:340(sin20)(54*9.8)=645.5
fk:.4(645.5)=258.2
a:(340(sin20)-258.2)/54=1.14
To set up the equation, we need to consider the forces acting on the object. From the information provided, we have the following forces:
1. The force pushing the box downwards, which has a magnitude of 340 N.
2. The normal force, which acts perpendicular to the surface the box is on.
3. The force of friction, which opposes the motion of the box and is proportional to the normal force.
Let's break down the forces:
1. The force pushing the box downwards can be resolved into two components: one perpendicular to the surface (normal force) and one parallel to the surface (force of friction). We will use the component parallel to the surface to calculate the acceleration.
2. The normal force acts perpendicular to the surface and balances the weight of the box. In this case, the normal force would be equal to the weight of the box, which can be calculated using the formula: weight = mass * gravitational acceleration. Thus, the normal force would be 54 kg * 9.8 m/s^2.
3. The force of friction can be calculated using the formula: force of friction = coefficient of friction * normal force. In this case, the coefficient of kinetic friction is given as 0.4, and we have already calculated the normal force.
Now, to find the acceleration, we need to use Newton's second law, which states that force equals mass times acceleration (F = ma). In this case, the net force acting in the direction of motion is the force pushing the box downwards (340 N) minus the force of friction. Rearranging the equation, we get:
340 N - force of friction = ma
Substituting the values we have:
340 N - (0.4 * normal force) = 54 kg * a
Now, solve this equation to find the acceleration of the box.