A mass of 30 kg lies on a horizontal surface with a coefficient of static friction of 0.72 and a coefficient of kinetic friction of 0.31. If a force of 25.1 Newtons is applied parallel to the surface (+x direction if you prefer), what is the magnitude of the acceleration of the object in m/s2?
To determine the magnitude of the acceleration of the object, we need to consider the forces acting on it and apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration, F_net = m * a.
First, let's determine the maximum force of static friction, F_static, that prevents the object from moving. The formula for the force of static friction is given by F_static = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force exerted by the surface on the object.
The normal force is equal to the gravitational force on the object, which is equal to the product of its mass and the acceleration due to gravity, N = m * g, where g is approximately 9.8 m/s^2. Substituting this into the formula for static friction, we have F_static = μ_s * m * g.
Calculating F_static, we have:
F_static = 0.72 * 30 kg * 9.8 m/s^2 = 211.68 N
Now, since the applied force of 25.1 N is less than the maximum static friction force of 211.68 N, the object will not move. Therefore, the acceleration of the object is zero in this case.
If the applied force were to exceed 211.68 N, the object would begin to move, and we would need to consider the force of kinetic friction instead.
The force of kinetic friction, F_kinetic, can be calculated using the formula F_kinetic = μ_k * N, where μ_k is the coefficient of kinetic friction. Since the object is already moving, the maximum force of kinetic friction is equal to the applied force, F_kinetic = 25.1 N.
With the force of kinetic friction, we can now calculate the net force, F_net, acting on the object by subtracting the force of kinetic friction from the applied force, F_net = F_applied - F_kinetic.
Calculating F_net, we have:
F_net = 25.1 N - 25.1 N = 0 N
Since the net force acting on the object is zero, and the object is already in motion, the acceleration of the object will also be zero in this case.
Therefore, the magnitude of the acceleration of the object in m/s^2 is 0 m/s^2.