a 20 N force pulls a 5kg box at a 60 degree angle above horizontal along the floor. If the Kinetic friction between contact surfaces is 2N. what is the acceleration of the box?
To find the acceleration of the box, we need to determine the net force acting on it. The net force is the vector sum of all the forces acting on the box.
First, let's resolve the 20 N force into its horizontal and vertical components. The horizontal component will cause the box to move along the floor, while the vertical component will cancel out because it is perpendicular to the direction of motion.
The horizontal component of the force can be found by multiplying the magnitude of the force (20 N) by the cosine of the angle (60 degrees):
Horizontal Force = 20 N * cos(60°)
Next, we need to consider the force of kinetic friction acting on the box. Since the box is moving, the friction force opposes the motion and acts in the opposite direction.
The friction force is given as 2 N. Since it is also in the horizontal direction, it will directly subtract from the horizontal component of the applied force.
Net Horizontal Force = Horizontal Force - Friction Force
Now, we can calculate the net force acting on the box by considering both the applied force and the force of friction.
Net Horizontal Force = (20 N * cos(60°)) - 2 N
To find the acceleration, we can use Newton's second law: F = ma, where F is the net force and m is the mass of the box. Rearranging the equation, we get:
a = F / m
Since we have the net force and the mass of the box, we can substitute them into the equation to find the acceleration.
Acceleration = Net Horizontal Force / mass
Acceleration = [(20 N * cos(60°)) - 2 N] / 5 kg