The coefficient of kinetic friction between a suitcase and the floor is 0.272. If the suitcase has a mass of 90.0 kg, how far can it be pushed across the level floor with 700 J of work?
W = d(coefficient of fk)(mg)
700 = d(.272)(90)(9.8)
d = 2.91m
Well, if the coefficient of kinetic friction is 0.272, then the floor is getting pretty friendly with that suitcase! They must be sliding along like a couple of smooth criminals.
Now, to figure out how far the suitcase can be pushed with 700 J of work, we'll have to do a little bit of math. The work done against friction can be calculated using the equation:
Work = Force of friction * distance
The force of friction, in this case, can be found using the equation:
Force of friction = coefficient of kinetic friction * normal force
Given that the normal force is equal to the weight of the suitcase (mass * gravity), we can substitute that in and solve for the force of friction.
Finally, once we know the force of friction, we can rearrange the first equation to solve for distance:
Distance = Work / Force of friction
So, let's plug in those values and calculate how far that suitcase can be pushed, shall we?
Force of friction = (0.272) * (mass * gravity)
= (0.272) * (90.0 kg * 9.8 m/s^2)
Now that we know the force of friction, we can calculate the distance:
Distance = 700 J / Force of friction
I'll leave the calculations up to you, my friend. Just remember to keep things friction-al!
To find the distance the suitcase can be pushed across the level floor, we can use the work-energy principle. The work done on an object equals the change in its kinetic energy.
The equation for work done on an object is given by:
Work = Force x Distance
The force exerted on the suitcase can be calculated using the formula for friction force:
Force of friction = coefficient of friction x normal force
The normal force is equal to the weight of the suitcase, which is given by:
Weight = mass x acceleration due to gravity
Using these formulas, we can calculate the force of friction and the distance the suitcase can be pushed.
1. Calculate the weight of the suitcase:
Weight = mass x acceleration due to gravity
Weight = 90.0 kg x 9.8 m/s^2
Weight = 882 N
2. Calculate the force of friction:
Force of friction = coefficient of friction x normal force
Force of friction = 0.272 x 882 N
Force of friction = 239.904 N
3. Calculate the distance the suitcase can be pushed:
Work = Force x Distance
700 J = 239.904 N x Distance
Distance = 700 J / 239.904 N
Distance = 2.919 m
Therefore, the suitcase can be pushed approximately 2.919 meters across the level floor with 700 J of work.
To find out how far the suitcase can be pushed across the level floor, we need to use the concept of work and energy.
The work done on an object is equal to the force applied multiplied by the distance traveled in the direction of the force. Mathematically, it can be represented as:
Work = Force × Distance
In this case, the work done on the suitcase is given as 700 J (Joules).
The force acting on the suitcase is the force of friction, which can be calculated using the equation:
Force of friction = coefficient of kinetic friction × normal force
The normal force is the force exerted by the floor on the suitcase, which is equal to the weight of the suitcase. The weight is calculated using the equation:
Weight = mass × gravitational acceleration
Given that the mass of the suitcase is 90.0 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can find the weight:
Weight = 90.0 kg × 9.8 m/s^2
Now, we can calculate the force of friction:
Force of friction = 0.272 × Weight
Once we have the force of friction, we can rearrange the work equation to find the distance:
Distance = Work / Force
Substituting the known values:
Distance = 700 J / Force of friction
Now, let's plug in the values and calculate the distance:
Weight = 90.0 kg × 9.8 m/s^2
Force of friction = 0.272 × Weight
Distance = 700 J / Force of friction
After calculating the values, we find the distance the suitcase can be pushed across the level floor with 700 J of work.