A box with a mass of 5 kg rests on a ramp with incline of 30 degrees. Calculate the maximum static force to keep the box from sliding dawn the rope.
To calculate the maximum static force required to keep the box from sliding down the ramp, we need to consider the forces acting on the box.
The force due to gravity can be decomposed into two components: the force acting perpendicular to the ramp (Fn) and the force acting parallel to the ramp (Fp). The force parallel to the ramp is the force that we need to counteract to prevent the box from sliding.
The formula to calculate the force parallel to the ramp is Fp = m * g * sin(theta), where m is the mass of the box, g is the acceleration due to gravity (approximately 9.8 m/s^2), and theta is the angle of incline (30 degrees).
In this case, the mass of the box is given as 5 kg and the angle of incline is 30 degrees. Plugging these values into the formula, we have:
Fp = 5 kg * 9.8 m/s^2 * sin(30 degrees)
To calculate sin(30 degrees), we can use a mathematical calculator or table, or we can use the fact that sin(30 degrees) is equal to 1/2.
Therefore, Fp = 5 kg * 9.8 m/s^2 * 1/2 = 24.5 N
So, the maximum static force required to keep the box from sliding down the ramp is 24.5 Newtons.
force down slope = 5*9.81* sin 30
= 5*9.81*.5
= 24.5 N