91Ó°ÊÓ

The normal force is an essential concept when analyzing motion, especially when friction is involved. In simple terms, the normal force is the force exerted by a surface to support the weight of an object resting on it. For the baseball player sliding, the normal force comes from the ground pushing up against him.
To find the normal force acting on the player, you calculate the gravitational force. This can be done using the equation:

• \( N = mg \)

where

• \( m \) is the mass of the player (81 kg) and
• \( g \) is the acceleration due to gravity (approximated as 9.8 m/s²).

Essentially, the normal force counters the force of gravity, preventing the player from sinking into the ground. This calculation gives a normal force of \( N = 793.8 \) N for our sliding player.Understanding normal force is crucial because it directly influences frictional force, as we'll see in the next section.

Frictional force is the resistance force that acts in the opposite direction of motion when an object slides over a surface. In this context, the frictional force is the force that slows down our baseball player as he slides into second base.
To calculate frictional force, you use the formula:

• \( f = \mu N \)

where

• \( \mu \) is the coefficient of kinetic friction (0.49 in this case), and
• \( N \) is the normal force calculated previously (793.8 N).

This yields a frictional force of \( f = 389.962 \) N for the sliding player.
Frictional force is key to understanding how objects cease to move, as it is the primary force that acts to bring sliding objects to a stop.

Initial velocity refers to the speed at which an object begins its motion. In the case of our sliding baseball player, it's the speed he had just before he began slowing down due to friction.
Given that the player comes to rest after 1.6 seconds, we use the following equation to find the initial velocity:

• \( v = vâ‚€ + at \)

where:

• \( v \) is the final velocity (0 m/s, as he comes to rest),
• \( vâ‚€ \) is the initial velocity,
• \( a \) is acceleration, and
• \( t \) is the time duration (1.6 s).

By rearranging and substituting the known values, we solve for \( vâ‚€ \). Understanding initial velocity is crucial as it helps determine how fast the player was moving before any other forces (like friction) started acting on him.

Acceleration is a measure of how quickly the velocity of an object changes. For the baseball player, it's the rate at which he slows down, i.e., comes to rest due to friction.
The equation for calculating acceleration is:

• \( a = \frac{f}{m} \)

where:

• \( f \) is the frictional force (389.962 N), and
• \( m \) is the mass of the object (81 kg).

Using these values, the acceleration is found to be \( a = \frac{389.962}{81} \) m/s².
Understanding acceleration is important in this scenario as it describes how the velocity decreases over time, bringing the player to a stop in the given timeframe.