Two crates, of mass m1 = 60 kg and m2 = 130 kg, are in contact and at rest on a horizontal surface (Fig. 4-54). A 620 N force is exerted on the 60 kg crate. The coefficient of kinetic friction is 0.15.
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To solve this problem, we need to calculate the net force acting on the system of two crates and determine if there is any motion.
1. Calculate the gravitational force acting on each crate:
The gravitational force is given by the equation F_gravity = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
For the 60 kg crate:
F_gravity_1 = m1 * g = 60 kg * 9.8 m/s^2
For the 130 kg crate:
F_gravity_2 = m2 * g = 130 kg * 9.8 m/s^2
2. Calculate the force of kinetic friction:
The force of kinetic friction is given by the equation F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force acting on the crate.
The normal force for the 60 kg crate is equal to the gravitational force acting on it:
F_normal_1 = F_gravity_1
The normal force for the 130 kg crate is equal to the sum of the gravitational forces acting on both crates:
F_normal_2 = F_gravity_1 + F_gravity_2
Now, calculate the force of kinetic friction for each crate:
F_friction_1 = μ * F_normal_1 = 0.15 * F_normal_1
F_friction_2 = μ * F_normal_2 = 0.15 * F_normal_2
3. Determine the net force:
The net force acting on the system of crates is calculated by subtracting the force of kinetic friction from the applied force:
Net force = Applied force - Sum of frictional forces
Net force = 620 N - (F_friction_1 + F_friction_2)
4. Determine if there is any motion:
If the net force is greater than zero, then the system of crates will experience motion. If the net force is less than or equal to zero, then the crates will stay at rest.
If the net force is greater than zero, calculate the acceleration of the system using Newton's second law of motion: F_net = m_total * a, where m_total is the total mass of both crates.
If the net force is less than or equal to zero, the system of crates will remain at rest.
Note: The given information does not specify the direction of the applied force. Make sure to consider the sign (positive or negative) of the force accordingly.