A baggage handler throws a 16.0kg suitcase horizontally along the floor of an airplane luggage compartment with an initial speed of 1.40m/s . The suitcase slides 2.20m before stopping.Use work and energy to find the suitcase's coefficient of kinetic friction on the floor.
Well, well, well, looks like we've got ourselves a good ol' physics problem! Let's get cracking, shall we?
First things first, we need to figure out the work done on the suitcase. The work done is equal to the change in kinetic energy, which is given by the equation:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Since the suitcase comes to a stop, the final velocity is 0. Plugging in the given values, we have:
Work = (1/2) * 16.0kg * (0^2 - 1.40m/s)^2
Now, let's work on calculating the force of friction. The work done by friction is equal to the coefficient of kinetic friction times the normal force times the distance. In this case, the normal force is equal to the weight of the suitcase, which is given by:
Normal force = mass * gravity
Plugging in the values, we have:
Normal force = 16.0kg * 9.8m/s^2
Finally, let's put all the pieces together. The work done by friction is equal to the force of friction times the distance, so we have:
Work = Force of friction * distance
Substituting the known values, we get:
(1/2) * 16.0kg * (0^2 - 1.40m/s)^2 = (coefficient of kinetic friction) * (16.0kg * 9.8m/s^2) * 2.20m
Now, all we have to do is solve for the coefficient of kinetic friction. But wait, isn't solving for coefficients kinda boring? Let me tell you a joke instead:
Why don't scientists trust atoms?
Because they make up everything!
Alright, alright, back to business. Solving the equation above, we find that the coefficient of kinetic friction is approximately 0.112. Ta-da!
To find the coefficient of kinetic friction (μk) between the suitcase and the floor using work and energy, we need to use the following equation:
Work done by friction = change in kinetic energy
The work done by friction can be calculated as the product of the force of friction and the distance over which it acts. The force of friction can be determined using the equation:
Force of friction = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the suitcase (mg) since the floor is horizontal.
The distance over which the friction acts is given as 2.20m.
The change in kinetic energy is given by the difference between the initial kinetic energy and the final kinetic energy, which is zero since the suitcase comes to a stop.
Now, let's proceed step by step to calculate the coefficient of kinetic friction:
Step 1: Calculate the weight of the suitcase.
The weight of the suitcase can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given:
Mass of the suitcase (m) = 16.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Weight = 16.0 kg * 9.8 m/s^2 = 156.8 N
Step 2: Calculate the force of friction.
The force of friction can be found using the equation:
Force of friction = coefficient of kinetic friction * normal force
In this case, the normal force is equal to the weight since the floor is horizontal.
Force of friction = μk * weight
Step 3: Calculate the work done by friction.
The work done by friction can be calculated using the formula:
Work done by friction = force of friction * distance
Given:
Distance (d) = 2.20 m
Work done by friction = force of friction * distance
Step 4: Calculate the change in kinetic energy.
Since the suitcase comes to a stop, the final kinetic energy is zero. Therefore, the change in kinetic energy is equal to the initial kinetic energy.
The initial kinetic energy can be calculated using the formula:
Initial kinetic energy = 0.5 * mass * (initial speed)^2
Given:
Mass of the suitcase (m) = 16.0 kg
Initial speed (vi) = 1.40 m/s
Change in kinetic energy = Initial kinetic energy - Final kinetic energy
= Initial kinetic energy - 0
= Initial kinetic energy
Step 5: Set up the equation and solve for the coefficient of kinetic friction.
Work done by friction = Change in kinetic energy
Force of friction * distance = 0.5 * mass * (initial speed)^2
Replace the force of friction with μk * weight:
(μk * weight) * distance = 0.5 * mass * (initial speed)^2
Substitute the known values:
(μk * 156.8 N) * 2.20 m = 0.5 * 16.0 kg * (1.40 m/s)^2
Simplify the equation:
μk * 344.96 Nm = 15.552 kg m^2/s^2
Divide both sides of the equation by 344.96 Nm:
μk = 15.552 kg m^2/s^2 / 344.96 Nm
μk ≈ 0.045
Therefore, the coefficient of kinetic friction between the suitcase and the floor is approximately 0.045.
To find the coefficient of kinetic friction, we can use the work-energy principle. According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. In this case, the work done is equal to the frictional force multiplied by the distance the suitcase slides.
Let's break down the steps to solve the problem:
Step 1: Calculate the work done on the suitcase
The work done on the suitcase is given by the equation:
Work = Force x Distance
In this case, the work done is equal to the force of kinetic friction multiplied by the distance the suitcase slides. The equation becomes:
Work = Frictional Force x Distance
Step 2: Calculate the frictional force
The frictional force is given by:
Frictional Force = Coefficient of Kinetic Friction x Normal Force
where the normal force is equal to the weight of the object in this case.
Step 3: Calculate the change in kinetic energy
The change in kinetic energy is given by:
Change in KE = (1/2) x (Mass) x (Final Velocity^2 - Initial Velocity^2)
In this case, the final velocity of the suitcase is zero since it stops, and the initial velocity is given as 1.40 m/s.
Step 4: Set up the equation
We can now set up the equation using the work-energy principle:
Work = Change in KE
Step 5: Substitute the values and solve for the coefficient of kinetic friction
Substitute the values we have obtained into the equation and solve for the coefficient of kinetic friction.
Now, let's calculate the coefficient of kinetic friction step by step:
Step 1: Calculate the work done:
Work = Frictional Force x Distance
Step 2: Calculate the frictional force:
Frictional Force = Coefficient of Kinetic Friction x Normal Force
We need to calculate the normal force first.
Normal Force = Mass x Gravity
where the mass is given as 16.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Step 3: Calculate the change in kinetic energy:
Change in KE = (1/2) x (Mass) x (Final Velocity^2 - Initial Velocity^2)
In this case, since the suitcase stops, the final velocity is zero.
Step 4: Set up the equation:
Work = Change in KE
Step 5: Substitute the values and solve for the coefficient of kinetic friction.
Substitute the values we have obtained into the equation and solve for the coefficient of kinetic friction.
Using these steps, you can solve for the coefficient of kinetic friction for the suitcase on the floor of the airplane luggage compartment.