The horizontal surface on which the block of mass 3.1 kg slides is frictionless. The force of 65 N acts on the block in a horizontal direction
and the force of 195 N acts on the block at an 60 angle as shown below.
What is the magnitude of the resulting acceleration of the block? The acceleration of gravity is 9.8 m/s^2.
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. We can break down the forces acting on the block into horizontal and vertical components.
First, let's determine the horizontal force acting on the block. The force of 65 N acts horizontally, so it contributes to the horizontal force. The force of 195 N at a 60° angle can be broken down into its horizontal and vertical components. The horizontal component can be calculated using the formula:
Horizontal component = Force * cos(angle)
Horizontal component = 195 N * cos(60°)
Next, let's calculate the net horizontal force acting on the block by summing up the individual horizontal forces:
Net horizontal force = Horizontal component from 65 N force + Horizontal component from 195 N force
Now, once we have the net horizontal force, we can calculate the resulting acceleration using Newton's second law:
Resultant acceleration = Net horizontal force / mass of the block
Substitute the given values into the equations, calculate the horizontal component, the net horizontal force, and lastly, the resulting acceleration.
Let's proceed with the calculations:
Horizontal component = 195 N * cos(60°)
Horizontal component = 195 N * 0.5
Horizontal component = 97.5 N
Net horizontal force = 65 N + 97.5 N
Net horizontal force = 162.5 N
Resultant acceleration = Net horizontal force / mass of the block
Resultant acceleration = 162.5 N / 3.1 kg
Resultant acceleration ≈ 52.42 m/s²
Therefore, the magnitude of the resulting acceleration of the block is approximately 52.42 m/s².