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using a horizontal force of 200N, we intend to move a wooden cabinate across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet ................
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Verified answer
Explanation:
To move the wooden cabinet across the floor at a constant velocity, we need to overcome the force of static friction. The static friction force opposes the applied force and prevents the cabinet from moving until the force applied is greater than or equal to the maximum static friction force. Once the applied force exceeds this maximum value, the cabinet will start moving, and the friction force will switch to the kinetic friction force, which is generally lower than the static friction force.
The formula to calculate the maximum static friction force is:
Maximum static friction force (F_static_max) = coefficient of static friction (μ_static) * normal force (N)
Where:
- Coefficient of static friction (μ_static) is a dimensionless constant that depends on the nature of the surfaces in contact. Since the surfaces are not specified, I'll assume a typical value for wood on wood, which is around 0.5 to 0.8.
- Normal force (N) is the force exerted by the floor on the cabinet perpendicular to the surface.
Assuming the cabinet is not accelerating vertically (it remains on the floor without lifting off), the normal force is equal in magnitude but opposite in direction to the force due to gravity acting on the cabinet, which is given by:
Force due to gravity (F_gravity) = mass of the cabinet (m) * gravitational acceleration (g)
Where:
- Gravitational acceleration (g) is approximately 9.81 m/s² on Earth's surface.
Now, we need to calculate the force due to gravity, then the maximum static friction force. If the applied force is less than or equal to the maximum static friction force, the cabinet will not move at a constant velocity.
Let's assume the mass of the cabinet is 50 kg (you can use the actual mass for your case if available):
1. Calculate the force due to gravity:
F_gravity = 50 kg * 9.81 m/s² ≈ 490.5 N
2. Calculate the maximum static friction force (assuming μ_static = 0.6):
F_static_max = 0.6 * 490.5 N ≈ 294.3 N
Since the applied horizontal force of 200 N is less than the maximum static friction force, the cabinet will not move at a constant velocity. If you want to move the cabinet at a constant velocity, you need to increase the applied force to overcome the static friction and then maintain a force equal to or slightly higher than the kinetic friction force while moving. The kinetic friction force is typically lower than the static friction force but remains roughly constant once the object is in motion.
Answer:
To determine the friction force exerted on the wooden cabin, we need to know the coefficient of friction between the cabin and the surface it is being moved across. The coefficient of friction is a dimensionless value that represents the interaction between two surfaces in contact.
Assuming we have the coefficient of friction (let's denote it as "μ"), we can calculate the friction force using the formula:
Friction force = Coefficient of friction * Normal force
The normal force is the force exerted by the surface on the cabin perpendicular to the surface. In this case, since the cabin is being moved horizontally at a constant velocity, the normal force is equal in magnitude and opposite in direction to the vertical force due to gravity acting on the cabin.
However, without information about the weight of the cabin or any other specifics, we cannot determine the exact normal force or the value of the friction force. Additionally, the coefficient of friction depends on the nature of the surfaces in contact, which also requires specific information.
In summary, to calculate the friction force exerted on the cabin, we need the coefficient of friction and the weight of the cabin or any information that allows us to determine the normal force.