Static Friction
Static friction is the force that counteracts the initiation of movement. It's why a block doesn’t slide when resting on a surface until a certain force threshold is surpassed. This frictional force depends on the surfaces in contact and is characterized by the coefficient of static friction, represented by \( \mu_s \). Static friction acts to resist motion up to a maximum value.
In this exercise, we calculate it using the formula: \( f_s = \mu_s N \). Here the normal force \( N \) is equivalent to the block’s weight due to gravity, calculated by \( N = mg \). For a 4.6 kg block, the force needed to start it moving (i.e., to overcome static friction) is 15.778 N.
To achieve this, the applied force must reach or exceed this static friction level. Once surpassed, static friction no longer holds the block in place.
Kinetic Friction
Once the block is in motion, the force that opposes its movement changes from static to kinetic friction. This friction is often less than static friction, which explains why less force is needed to continue moving the block than to start it moving. The coefficient of kinetic friction \( \mu_k \) characterizes this friction and is used alongside the normal force \( N \) to find the force of kinetic friction \( f_k = \mu_k N \).
In our example, with \( \mu_k = 0.22 \) and a normal force of 45.08 N, kinetic friction calculates to 9.9176 N. The block continues to experience this resistance as long as it slides. Importantly, unlike static friction, kinetic friction doesn’t change with the speed of the block.
If the applied force were equal to kinetic friction, the block would move at a constant velocity. However, since the applied force here exceeds kinetic friction, it leads to acceleration.
Newton's Laws of Motion
Newton's laws are fundamental in understanding how forces affect motion. Specifically, his second law is essential here: the acceleration \( a \) of an object is directly proportional to the net force, \( F_{net} \), acting on it and inversely proportional to its mass \( m \), expressed as \( F = ma \).
By analyzing the forces acting on the block, including both applied and frictional forces, we determine the net force. This net force then dictates whether and how the block accelerates.
In this exercise, after applying the initial force, the block experiences a net force greater than zero due to the difference between the applied force and the kinetic friction. Thus, according to Newton’s second law, the block doesn't move with constant velocity; it accelerates, confirming the law’s predictions.
Acceleration
Acceleration is the rate at which the velocity of an object changes over time due to applied forces. In the context of this exercise, after overcoming static friction, the block experiences acceleration.
Once the block starts sliding, the force continuing to act (15.778 N) is more than what is needed to merely oppose kinetic friction (9.9176 N). This difference results in a net force which accelerates the block according to Newton's second law.
We calculate its acceleration at 1.274 \( \text{m/s}^2 \), using the formula \( a = F_{net}/m \). This acceleration signifies a continuous increase in velocity, assuming the applied force stays constant and does not light up.
