A 66-kg baseball player slides into third base. He starts his slide at a speed of 4.3 m/s and his speed is zero just as he reaches the base. If the coefficient of friction between his clothes and the surface of the baseball infield is 0.60, determine the following.
(a) mechanical energy lost due to friction acting on the player
J
(b) distance he slides
m
a. KE = 0.5*M*V^2 = 0.5*66*4.3^2 = 610.2 J. = Energy lost due to friction.
b. M*g = 66 * 9.8 = 646.8 N. = Wt. of runner = Normal(Fn).
Fk = u*Fn = 0.6 * 646.8 = 388.1 N. = Force of kinetic friction.
KE = Fk*d = 610.2
388.1*d = 610.2
d = 1.57 m.
Well, let's calculate the answers, but first I have a joke for you:
Why don't scientists trust atoms?
Because they make up everything!
Now let's get back to the question. To find the answers, we can use the work-energy theorem.
(a) The work done by friction is equal to the change in mechanical energy of the player. Since the initial kinetic energy is converted entirely into work done by friction, we can calculate it using the equation:
Work done by friction = Change in kinetic energy
The initial kinetic energy can be calculated using:
Initial kinetic energy = (1/2) * mass * (initial velocity)^2
Final kinetic energy is zero since the player comes to rest, so:
Change in kinetic energy = -Initial kinetic energy
Now let's do the calculations:
Initial kinetic energy = (1/2) * 66 kg * (4.3 m/s)^2
Now we know the initial kinetic energy, we can calculate the work done by friction:
Work done by friction = -Initial kinetic energy
(b) To find the distance the player slides, we can use the equation:
Work done by friction = Force of friction * distance
Since the work done by friction is equal to the change in kinetic energy, we can rewrite the equation as:
Change in kinetic energy = Force of friction * distance
Now let's calculate the force of friction:
Force of friction = coefficient of friction * Normal force
The Normal force can be calculated using:
Normal force = mass * gravitational field strength
Now we have all the information to calculate the distance:
Change in kinetic energy = Force of friction * distance
Remember to use the negative sign for the change in kinetic energy.
Now let's crunch the numbers and calculate the answers!
To determine the mechanical energy lost due to friction acting on the player, we can use the formula for work done by friction. The work done by friction is given by the equation:
Work = Force of friction * distance
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction * Normal force
The normal force is equal to the weight of the player, which can be calculated as:
Normal force = mass * acceleration due to gravity
So, we have:
Force of friction = coefficient of friction * (mass * acceleration due to gravity)
Next, we need to find the distance over which the work is done. Since the player's speed is zero just as he reaches the base, we can assume that the friction force acts over the entire distance of the slide.
The distance can be calculated using the basic equation of motion:
vf^2 = vi^2 + 2 * acceleration * distance
Since the player's final velocity (vf) is zero, and his initial velocity (vi) is 4.3 m/s, we can rearrange the equation to solve for distance:
distance = (vf^2 - vi^2) / (2 * acceleration)
Now, let's calculate the values step by step.
(a) Mechanical energy lost due to friction acting on the player:
Mass = 66 kg
Coefficient of friction = 0.60
Acceleration due to gravity = 9.8 m/s^2
Force of friction = 0.60 * (66 kg * 9.8 m/s^2)
Force of friction = 382.8 N
Distance is equal to the distance he slides.
(b) Distance he slides:
Initial velocity (vi) = 4.3 m/s
Final velocity (vf) = 0 m/s
Distance = (vf^2 - vi^2) / (2 * acceleration)
Distance = (0^2 - 4.3^2) / (2 * acceleration)
Distance = (-4.3^2) / (2 * acceleration)
Distance = 9.29 / (2 * acceleration)
Therefore, the distance he slides is 4.174 meters.
To summarize:
(a) The mechanical energy lost due to friction acting on the player is approximately 382.8 Joules.
(b) The distance he slides is approximately 4.174 meters.
To determine the mechanical energy lost due to friction acting on the player, we can use the concept of work done by friction. The work done by friction can be calculated using the equation:
Work done by friction = force of friction × distance
To find the force of friction, we need to calculate the normal force acting on the player. The normal force is equal to the weight of the player, which can be calculated by multiplying the mass (66 kg) by the acceleration due to gravity (approximately 9.8 m/s^2).
Normal force = mass × acceleration due to gravity
Next, we can calculate the force of friction using the equation:
Force of friction = coefficient of friction × normal force
Now, we can calculate the work done by friction using the equation mentioned earlier.
(a) Mechanical energy lost due to friction acting on the player:
Work done by friction = Force of friction × distance
To find the distance, we need to use the equation for the work done by friction, rearranged to solve for distance.
Distance = Work done by friction / Force of friction
Let's plug in the given values:
Mass = 66 kg
Initial speed = 4.3 m/s
Coefficient of friction = 0.60
Acceleration due to gravity = 9.8 m/s^2
First, we find the normal force:
Normal force = mass × acceleration due to gravity
Normal force = 66 kg × 9.8 m/s^2
Next, we find the force of friction:
Force of friction = coefficient of friction × normal force
Force of friction = 0.60 × (66 kg × 9.8 m/s^2)
Finally, we calculate the work done by friction:
Work done by friction = Force of friction × distance
To find the distance, rearrange the equation:
Distance = Work done by friction / Force of friction
Now, plug the values into the equation and calculate the answer.
(b) Distance he slides:
Distance = Work done by friction / Force of friction
Let's calculate the distance.
Consider a situation where a baseball player slides to a stop on level ground. Using
energy considerations, calculate the distance the 65.0 kg baseball player slides, given that
his initial speed is 6.0 m/s and the force of friction against him is a constant 450 N