A block of mass m=8 kg is held at the rest on a smooth (fiction less) 37 degree incline by a horizontal force F. the magnitude of the force F (in N) is:
To find the magnitude of the force F required to hold the block at rest on the incline, we need to analyze the forces acting on the block.
First, let's consider the weight of the block, which is given by the formula:
Weight = mass x acceleration due to gravity
Since the block is on an incline, we need to break down the weight into two components: one parallel to the incline and one perpendicular to the incline.
The perpendicular component of the weight can be found using the formula:
Perpendicular component = weight x cos(θ)
where θ is the angle of inclination (37 degrees in this case).
The parallel component of the weight can be found using the formula:
Parallel component = weight x sin(θ)
Next, since the block is at rest, the net force acting on the block must be zero. This means that the force F, along with the perpendicular component of the weight, must balance out the parallel component of the weight.
So we can set up an equation:
Force F = Parallel component of weight
Force F = weight x sin(θ)
Now, let's calculate the magnitude of the force F using the given information:
Mass of the block, m = 8 kg
Angle of inclination, θ = 37 degrees
Acceleration due to gravity, g = 9.8 m/s^2
Weight = mass x acceleration due to gravity
Weight = 8 kg x 9.8 m/s^2
Perpendicular component = Weight x cos(θ)
Perpendicular component = (8 kg x 9.8 m/s^2) x cos(37 degrees)
Parallel component = Weight x sin(θ)
Parallel component = (8 kg x 9.8 m/s^2) x sin(37 degrees)
Force F = Parallel component
Force F = (8 kg x 9.8 m/s^2) x sin(37 degrees)
Now, we can calculate the magnitude of the force F:
Force F = (8 kg x 9.8 m/s^2) x sin(37 degrees)
Simplifying this equation will give you the magnitude of the force F in Newtons.