the wooden crate in the figure below has a mass of 40kg. How much horizontal force is needed to A. start it moving B. to keep it moving along the wood floor at a constant speed
To determine the amount of horizontal force needed to start the wooden crate moving, we can use the concept of static friction. The force required to overcome static friction is known as the force of static friction.
A. To start the crate moving:
The force needed to start the crate moving is equal to the force of static friction. The force of static friction can be calculated using the equation:
\(F_{\text{static}} = \mu_s \times N\)
where \(F_{\text{static}}\) is the force of static friction, \(\mu_s\) is the coefficient of static friction, and \(N\) is the normal force.
The coefficient of static friction (\(\mu_s\)) is a property of the surface in contact. If it is not provided, you need to look up the coefficient of static friction between wood and the floor in question.
The normal force (\(N\)) can be calculated using the equation:
\(N = m \times g\)
where \(m\) is the mass of the crate and \(g\) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)).
Substitute the given values into the equations and calculate the force of static friction.
B. To keep the crate moving at a constant speed:
Once the crate is already in motion, the force required to keep it moving at a constant speed is equal to the force of kinetic friction. The force of kinetic friction can be calculated using the equation:
\(F_{\text{kinetic}} = \mu_k \times N\)
where \(F_{\text{kinetic}}\) is the force of kinetic friction, \(\mu_k\) is the coefficient of kinetic friction, and \(N\) is the normal force.
Similar to the coefficient of static friction, you need to look up the coefficient of kinetic friction between wood and the floor in question if it is not provided.
The normal force can be calculated in the same way as before, \(N = m \times g\).
Once you have the coefficient of kinetic friction (\(\mu_k\)) and the normal force (\(N\)), substitute these values into the equation and calculate the force of kinetic friction.
Remember, to keep the crate moving at a constant speed, the applied force needs to match the force of kinetic friction.