a box of mass 10kg is at rest on a horizontal plane.a force of 20N is applied to it at 30 degrees to the plane.assuming there no frictional force between the box and the plane,calculate the acceleration of the box.
f=ma
20*cos30=10*a
solve for a.
Use;
revolving into x-axis
Wsin@ - Pcos@=ma
To calculate the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
Net force = mass x acceleration
In this case, the net force acting on the box is the component of the applied force that is parallel to the horizontal plane. Since there is no friction, the only force acting on the box is the applied force.
To find the component of the force parallel to the horizontal plane, we can use trigonometry:
Component of force parallel to the plane = Force x cos(angle)
Given:
Mass of the box (m) = 10 kg
Applied force (F) = 20 N
Angle (θ) = 30 degrees
First, let's calculate the component of the force parallel to the plane:
Component of force parallel to the plane = 20 N x cos(30 degrees)
Using the cosine value of 30 degrees (which is √3/2), we can calculate:
Component of force parallel to the plane = 20 N x (√3/2) = 10√3 N
Now we can substitute the values into Newton's second law and solve for the acceleration:
Net force = mass x acceleration
10√3 N = 10 kg x acceleration
Rearranging the equation to solve for acceleration:
acceleration = (10√3 N) / (10 kg)
Simplifying:
acceleration = √3 m/s²
Therefore, the acceleration of the box is approximately √3 m/s² when a force of 20 N is applied at 30 degrees to the plane, assuming no friction.