A box with a mass of 10 kg rests on a frictionless surface which makes an angle of 60⁰ with horizontal. How large a force must be applied to the box, parallel to the incline to hold the box stationary on the inclined plane?
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Answer:
To find the force required to hold the box stationary on the inclined plane we need to analyze the forces acting on the box.
Let's break down the gravitational force into components. The weight of the box can be divided into two components: one parallel to the incline and one perpendicular to the incline.
The component of the weight acting parallel to the incline is given by: F_par = m * g * sin(θ where m is the mass of the box g is the acceleration due to gravity (approximately 9.8 m/s² and θ is the angle of the incline (60° in this case).
Substituting the given values into the equation we have: F_par = 10 kg * 9.8 m/s² * sin(60°).
Using the trigonometric identity sin(60°) = √3 / 2 we can simplify the equation: F_par = 10 kg * 9.8 m/s² * (√3 / 2).
Calculating the value we get: F_par ≈ 84.81 N.
Therefore a force of approximately 84.81 N must be applied parallel to the incline to hold the box stationary.