Finding acceleration in spring situations

In summary, a duck with a mass of 40kg is being pulled by a spring with a spring constant of 900N/m. The coefficient of kinetic friction between the duck and the road is 0.6. With a spring stretch of 0.4m, the resulting acceleration of the duck is 3.1 m/s2.
  • #1
bunk66
4
0

Homework Statement


A duck of mass 40kg is being pulled by a spring with k = 900N/m. If μk = 0.6 between the duck and the road, find the acceleration of the duck given that the spring stretches 0.4m.

Homework Equations


Fspring = kx, where k = spring constant and x = stretch of spring
Fnet = ma

The Attempt at a Solution


Fspring = kx
F = 900N/m(0.6m)
F = 540N

That's about as far as I got before not knowing what to do next.
 
Last edited:
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  • #2
bunk66 said:
F = 900N/m(0.4m)
F = 540N
Those are two different forces, so give them different names.
In which directions do they act?
How do they relate to the acceleration of the duck?
 
  • #3
haruspex said:
Those are two different forces, so give them different names.
In which directions do they act?
How do they relate to the acceleration of the duck?
What exactly do you mean that they are two different forces? In the section that you quoted, isn't there only one force being calculated: the spring force?

And p.s, I made a typing error. Where it says 0.4, it should be 0.6
 
  • #4
bunk66 said:
I made a typing error. Where it says 0.4, it should be 0.6
OK, that's what made me think you were referring to two different forces.
So, what is the frictional force acting on the duck (direction and magnitude)?
 
  • #5
haruspex said:
OK, that's what made me think you were referring to two different forces.
So, what is the frictional force acting on the duck (direction and magnitude)?
I mixed some of the numbers apparently.

Fspring = kx
F = 900N/m(0.4m)
F = 360N

40kg x 9.8 = 392N

Ff = μk(FN)
Ff = 0.6(392N)
Ff = 236N

Fnet = Fa - Ff
Fnet = 360N - 236N
Fnet = 124N

Fnet = ma
Fnet/m = a
124N / 40kg = a
3.1 m/s2 = a

Evidently that was a lot easier than I made it out to be :redface:
 

1. How do I find the acceleration in a spring situation?

The acceleration in a spring situation can be found by dividing the force applied to the spring by the mass attached to the spring. This is represented by the equation a = F/m, where a is acceleration, F is force, and m is mass.

2. What is the formula for calculating spring acceleration?

The formula for calculating spring acceleration is a = F/m, where a is acceleration, F is force, and m is mass. This formula is derived from Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

3. Can the acceleration in a spring situation be negative?

Yes, the acceleration in a spring situation can be negative. This occurs when the force applied to the spring is opposite to the direction of motion of the mass attached to the spring. Negative acceleration indicates that the object is slowing down, while positive acceleration indicates that the object is speeding up.

4. How does the mass affect the acceleration in a spring situation?

The mass attached to the spring directly affects the acceleration in a spring situation. According to the formula a = F/m, as the mass increases, the acceleration decreases. This means that a heavier mass attached to the spring will have a lower acceleration compared to a lighter mass attached to the same spring.

5. How does the force applied to the spring affect the acceleration?

The force applied to the spring also directly affects the acceleration in a spring situation. As the force increases, the acceleration also increases. This is because a greater force will cause a greater change in the velocity of the mass attached to the spring, resulting in a higher acceleration.

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