Mechanical Energy of 56.9kg Exercise Machine in 71.2m Hall

In summary, the conversation discusses solving a problem involving moving an exercise machine with a mass of 56.9 kg down a 71.2 meter long hallway with a coefficient of friction of 0.866. The goal is to find the mechanical work done during this process. It is determined that the work can be calculated using the formula W = Ffriction * d, where the friction force is proportional to the weight of the machine and the distance traveled. The normal force due to gravity is used to calculate the friction force, and this can be found by multiplying the mass of the machine by the gravitational acceleration of 9.809 m/s2.
  • #1
map7s
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Homework Statement



NOTE: Use the local value of g = 9.809 m/s2
You and your roommate are dragging an exercise machine (mass 56.9 kg) down a 71.2 meter long hall, from the stair landing, where (because of union rules) the UPS driver left it, to your dorm room. The coefficient of friction with the floor is μ = 0.866. The mechanical work you do in the process is:

Homework Equations



ME=GPE+KE
GPE=mgy
KE=1/2 mv^2
F(friction)=mu*N
N=mg
F=ma
W=Fd

The Attempt at a Solution



I tried solving for the gravitational potential energy and then solving for the frictional force and multiplying the result by the distance...looking back on it, I'm fairly sure that it was probably the wrong method to go about this problem. I know that the mechanical energy is the sum of the potential energy and kinetic energy. However, if that is the case, I would have to solve for velocity and I am not sure how to do that with the information given. When I try to use the 2-d equations, I end up with two variables (v and vo). It would really help if I could get some help (and reasoning) about solving this problem.
 
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  • #2
Since one is moving the mass along the hallway, there is no change in elevation, therefore no change in GPE.

Apply W = Fd.

The force due to friction is simply [itex]\mu_k[/itex]N = [itex]\mu_k[/itex]mg.
 
  • #3
okay...that makes more sense...so in the equation W=Fd, for F, would I use ma where a=g? and then take that F value and subtract the force of friction from it and then multiply it by the distance?
 
  • #4
Assume the exercise machine is traveling at constant speed, i.e. no acceleration.

The friction force is proportional to the weight (N) of the machine. N is the normal force due to gravity, which is just m*g.

The work performed is the simply the product of the friction force times the distance travel. W = Ffriction * d. Find the friction force. Please refer to my previous post.
 
  • #5
oh...okay...that actually makes sense now...thank you so much! that was really helpful!
 

1. What is mechanical energy?

Mechanical energy is the energy possessed by an object due to its motion or position. It can be either potential energy, which is stored energy, or kinetic energy, which is the energy of motion.

2. How is mechanical energy calculated?

Mechanical energy can be calculated using the formula E = PE + KE, where E is the total mechanical energy, PE is the potential energy, and KE is the kinetic energy. Potential energy is calculated as mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. Kinetic energy is calculated as ½mv^2, where m is the mass of the object and v is its velocity.

3. What is the significance of the 56.9kg exercise machine in the 71.2m hall?

The 56.9kg exercise machine and the 71.2m hall are both important in determining the amount of mechanical energy present. The mass of the machine affects its potential and kinetic energy, while the length of the hall affects its potential energy. The combination of these factors helps to determine the total mechanical energy of the system.

4. How does the mechanical energy of the exercise machine change as it moves through the hall?

As the exercise machine moves through the hall, its mechanical energy will change. As it moves from a higher position to a lower position, its potential energy will decrease while its kinetic energy will increase. The opposite will happen as it moves from a lower position to a higher one. The total mechanical energy, however, will remain constant as long as there are no external forces acting on the machine.

5. Can the mechanical energy of the exercise machine be converted into other forms of energy?

Yes, the mechanical energy of the exercise machine can be converted into other forms of energy, such as thermal energy or sound energy. For example, when using the machine, friction between its moving parts will convert some of its mechanical energy into thermal energy. Additionally, if the machine is equipped with speakers, some of its mechanical energy can be converted into sound energy. However, the total mechanical energy of the system will still remain constant.

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