The horizontal surface on which the block of mass 5 kg slides is frictionless. The force of 29 N acts on the block in a horizontal direction and the force of 58 N acts on the block at an angle(top Right).
What is the magnitude of the resulting acceleration of the block?
To find the magnitude of the resulting acceleration of the block, you can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
First, let's resolve the force acting at an angle into its horizontal and vertical components. The force of 58 N can be resolved into its horizontal component (F_horizontal = F_cosθ) and vertical component (F_vertical = F_sinθ), where θ is the angle.
Given that the horizontal force (F_horizontal) is 29 N, we can determine the angle (θ) using the following equation:
F_horizontal = F * cosθ
29 N = 58 N * cosθ
Solving for cosθ gives us:
cosθ = 29 N / 58 N
cosθ ≈ 0.5
To find the angle θ, you can take the inverse cosine of 0.5:
θ ≈ cos^(-1)(0.5)
θ ≈ 60 degrees
Now that we have the angle, we can determine the vertical force (F_vertical) using the equation:
F_vertical = F * sinθ
F_vertical = 58 N * sin(60 degrees)
F_vertical ≈ 50.2 N
Since there is no friction, the only horizontal force acting on the block is the 29 N force. Now we can calculate the net force in the horizontal direction:
Net horizontal force = 29 N
Finally, we can calculate the resulting acceleration using Newton's second law:
Resulting acceleration = Net force / Mass
Resulting acceleration = (Net horizontal force) / (Mass)
Resulting acceleration = 29 N / 5 kg
Resulting acceleration ≈ 5.8 m/s²
Therefore, the magnitude of the resulting acceleration of the block is approximately 5.8 m/s².