If 4.5 kg object is sitting at rest on a 30 degree incline that has a coefficient of static friction of .19, what is the net force down the plane? Does it start sliding?
To find the net force down the plane, we first need to calculate the force of gravity acting on the object and the force of friction opposing its motion.
1. Calculate the Force of Gravity:
The force of gravity can be calculated using the formula: F_gravity = m * g, where m is the mass of the object (4.5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 4.5 kg * 9.8 m/s^2
F_gravity = 44.1 N
2. Calculate the Force of Friction:
The force of friction can be found using the formula: F_friction = μ * F_normal, where μ is the coefficient of static friction (0.19) and F_normal is the normal force exerted by the incline on the object. The normal force can be calculated using the equation: F_normal = m * g * cos(theta), where theta is the angle of the incline (30 degrees).
F_normal = 4.5 kg * 9.8 m/s^2 * cos(30 degrees)
F_normal = 38.15 N
F_friction = 0.19 * 38.15 N
F_friction = 7.25 N
3. Calculate the Net Force:
The net force down the plane can be calculated by subtracting the force of friction from the force of gravity because they act in opposite directions:
Net Force = F_gravity - F_friction
Net Force = 44.1 N - 7.25 N
Net Force = 36.85 N
If the net force down the plane is positive (in the direction of motion), it will start sliding. In this case, the net force is positive (36.85 N), indicating that the object will start sliding down the incline.
Therefore, the net force down the plane is 36.85 N, and the object will start sliding.