A file cabinet weighing 1500 N is at rest on the floor. The coefficient of static friction between the floor and the cabinet is 0.5. What is the minimum force required to make the file cabinet move horizontally
F - csf*N = 0
N - m*g = 0
where F is the force, csf is the coefficient of static friction, N is the normal force, m is the mass of the cabinet, and g is the gravitational constant.
To determine the minimum force required to make the file cabinet move horizontally, we need to calculate the maximum static friction force between the cabinet and the floor. The formula to calculate static friction force is:
Friction force = coefficient of static friction × normal force
First, we need to calculate the normal force acting on the file cabinet, which is equal to its weight. The weight of the file cabinet can be found using the formula:
Weight = mass × gravitational acceleration
Since the weight is given as 1500 N, we can calculate the mass of the file cabinet. Gravitational acceleration is typically assumed to be 9.8 m/s² on Earth.
Weight = mass × gravitational acceleration
1500 N = mass × 9.8 m/s²
Solving for mass:
mass = 1500 N / 9.8 m/s²
mass ≈ 153.06 kg
Next, we can calculate the maximum static friction force:
Friction force = coefficient of static friction × normal force
Friction force = 0.5 × 1500 N
Friction force = 750 N
Therefore, the minimum force required to make the file cabinet move horizontally is 750 N.
To find the minimum force required to make the file cabinet move horizontally, we need to consider the concept of static friction.
Static friction is the force that prevents two surfaces from sliding past each other when they are at rest. It can be modeled by the equation:
F_static = μ_static * N
where F_static is the force of static friction, μ_static is the coefficient of static friction, and N is the normal force perpendicular to the surfaces in contact.
In this case, the weight of the file cabinet (1500 N) is equal to the normal force (N) because the cabinet is at rest on the floor. Therefore, N = 1500 N.
Now, we can calculate the maximum force of static friction using the coefficient of static friction (μ_static = 0.5) and the normal force (N = 1500 N):
F_static = 0.5 * 1500 N
= 750 N
The maximum force of static friction is 750 N. This means that the file cabinet requires a minimum force of 750 N to overcome the force of static friction and start moving horizontally. Any force greater than 750 N will cause the file cabinet to move horizontally.