Work, Force, Acceleration, and speed of a box attached to a spring

In summary, the question deals with a 5.5kg box attached to a spring and a wall, with a force of 90N moving it 40cm away from equilibrium. The coefficient of kinetic friction is 0.300. The work done by the applied force is Fapplied, and the magnitude of friction can be found using the formula Ff=UkFn. The speed of the box at 40cm can be determined using conservation of energy, taking into account the energy from the force applied, friction, and the spring. However, the question is unsolvable without the value of k.
  • #1
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Homework Statement


A 5.5kg box is attached to a spring which is attached to a wall. The box is subject to a force of 90N moving it from its equilibrium to a position 40cm away, the coefficient of kinetic friction is 0.300.
a. what is the work done by the applied force over the 40 cm?
b.what is the magnitude of friction between box and surface?
c.what is the speed of the box at 40cm

*I appologize for my formulas looking this way I don't know how to make them look proper*

Homework Equations


a. work=F*dcos
b.Ff=UkFn (opposes motion)
c.conservation of energy
Ek=E(force applied)-Efriction-(Espring?)
Ek=0.5m(v)^2

The Attempt at a Solution


a. I know i have to use the work equation but my question is what is the force is it the Fapplied-Ffriction or just Fapplied?
b.Im pretty sure that this is just plug and chug with the formula where Fn=Fg
c. My only question is should I include the Espring in the calculation?

Thanks a lot in advance! :smile:
 
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  • #2

The Attempt at a Solution


a. I know i have to use the work equation but my question is what is the force is it the Fapplied-Ffriction or just Fapplied?

Since you're trying to find the work done by the applied force, it should be Fapplied. If you were trying to find the total work done on the box, it would be Fapplied-Ffriction.

b.Im pretty sure that this is just plug and chug with the formula where Fn=Fg

Yes.
c. My only question is should I include the Espring in the calculation?
Yes, because that's part of the energy of the system. However, the question doesn't provide k, and without this piece of information it's unsolvable. Is this a mistake on your part?
 
  • #3
ya that's my fault i was re-writing the question to make it shorter thank you for the help!
 

1. What is the relationship between work and force?

The relationship between work and force is defined by the equation W = Fd, where W represents work in joules, F represents force in newtons, and d represents displacement in meters. This means that the amount of work done on an object is directly proportional to the force applied and the distance over which the force is applied.

2. How do you calculate the acceleration of a box attached to a spring?

The acceleration of a box attached to a spring can be calculated using the equation a = F/m, where a represents acceleration in meters per second squared, F represents force in newtons, and m represents mass in kilograms. This means that the acceleration of the box is directly proportional to the force applied and inversely proportional to the mass of the box.

3. What is the speed of a box attached to a spring?

The speed of a box attached to a spring can be calculated using the equation v = ωA, where v represents speed in meters per second, ω represents angular frequency in radians per second, and A represents amplitude in meters. This means that the speed of the box is directly proportional to the angular frequency and amplitude of the spring's oscillations.

4. How does the force applied to a spring affect its acceleration?

The force applied to a spring directly affects its acceleration, as stated by Newton's Second Law of Motion (F = ma). This means that the greater the force applied to the spring, the greater its acceleration will be. However, once the spring reaches its maximum elastic limit, the acceleration will decrease due to the spring's stiffness.

5. Can the speed of a box attached to a spring be constant?

Yes, the speed of a box attached to a spring can be constant if the spring is in a state of equilibrium, meaning that the forces acting on the spring are balanced. In this case, the spring will not be oscillating and the speed of the box will remain constant. However, if a net force is applied to the spring, the speed of the box will change and the spring will begin to oscillate.

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