forces of 185N and 245N act east and south respectively on an 80 kg mass.If the force of friction is ZERO , find the accleration of the mass.
To find the acceleration of the mass, we'll use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, we have two forces acting on the mass: a force of 185N acting east and a force of 245N acting south. Since these forces are at right angles to each other, we can use vector addition to find their resultant force.
To find the acceleration, we need to calculate the net force acting on the mass. The net force is the vector sum of all the forces acting on the object.
Step 1: Resolve the forces into their horizontal (x) and vertical (y) components.
- The 185N force acting east only has an x-component, which is 185N.
- The 245N force acting south only has a y-component, which is -245N.
Step 2: Use the resolved components to find the resultant force.
- The x-component of the resultant force is the sum of the x-components of the individual forces, which is 185N.
- The y-component of the resultant force is the sum of the y-components of the individual forces, which is -245N.
Step 3: Calculate the net force using the resultant components.
- The net force is the square root of the sum of the squares of the x and y-components of the resultant force.
- Net force = sqrt((185N)^2 + (-245N)^2)
Step 4: Divide the net force by the mass to find the acceleration.
- Acceleration = Net force / Mass
- Acceleration = (sqrt((185N)^2 + (-245N)^2)) / 80kg
By following these steps and performing the calculations, you can find the acceleration of the mass.