Answer :
Answer: Respective answers are 1.27 m/s^2 and 90.17 N
Explanation:
Explanation requires basic knowledge of forces in physics. The solutions are attached in this response. To summarize:
- Newton's Second Law -> F = ma
- Force of friction = Fn (normal force) x µk (coefficient of kinetic friction)
- Because the surface is leveled, Fn = Fg, Fg = mg
- The crates exert the same amount of force on each other because of the rule of action // reaction (Newton's Third Law)
Final answer:
The acceleration of the system of two crates is approximately 0.809 m/s². Each crate exerts a force of approximately 57.44 N on the other, due to Newton's third law of motion.
Explanation:
To determine the acceleration of the system of two crates with masses m1 = 71 kg and m2 = 130 kg, we first need to compute the total force exerted on the system after accounting for kinetic friction. The coefficient of kinetic friction here is given as 0.18. Since the force F = 610 N is applied on the 71-kg crate, we need to subtract the frictional forces before calculating the net force.
The total mass of the system is m1 + m2 = 71 kg + 130 kg = 201 kg. The frictional force due to kinetic friction ([tex]f_{k}[/tex]) can be calculated using [tex]f_{k} = mu_{k}[/tex] * normal force. The normal force equals the total weight of the system, which is (m1 + m2) * g, where g = 9.8 m/s² is the acceleration due to gravity.
Frictional force for both crates: [tex]f_{k}[/tex] = 0.18 * (71 kg + 130 kg) * 9.8 m/s² = 447.48 N.
The acceleration (a) of the entire system can be calculated by the net force (F - [tex]f_{k}[/tex]) divided by the total mass (m1 + m2):
a = (610 N - 447.48 N) / 201 kg ≈ 0.809 m/s².
To find the magnitude of the force that each crate exerts on the other, we can use Newton's third law, which states that all forces between two objects are equal in magnitude and opposite in direction. Therefore, if we assume F is exerted to the right on the 71-kg crate, then this crate exerts a force of equal magnitude to the left on the 130-kg crate and vice versa.
Using the found acceleration, we can calculate the force the 71-kg crate experiences (F1):
F = m1 * a
F1 = 71 kg * 0.809 m/s² ≈ 57.44 N.
Therefore, the 71-kg crate exerts a force of approximately 57.44 N on the 130-kg crate, and by Newton's third law, the 130-kg crate exerts an equal and opposite force on the 71-kg crate.
