Find Displacement given force

In summary, to find Δx for the given scenario, we need to use the equations F=ma and dx/dt=[(-T)Fx/m]e-(t/T)+v0. By integrating both sides and taking the definite integral between t0 and tf, we get x=[(T2)Fx)/m]e-(t/T)+v0t. However, the constant of integration is not equal to v0, and must be solved for separately. After solving for the constant, the final equation for Δx is x=v0+[(TFx)/m](1-e-t/T).
  • #1
getty102
38
0

Homework Statement


Find Δx
Given:
Fxe-(t/T)
v0=-41.2 m/s
tf=84.54 s
T=46 s
Fx=13.4 N
m=8.8 kg



Homework Equations


F=ma


The Attempt at a Solution


a=Fxe-(t/T)/m
dv/dt=Fxe-(t/T)/m

*integrate both sides*
v=[(-T)Fx)/m]e-(t/T)+v0
dx/dt=[(-T)Fx/m]e-(t/T)+v0

*take the definite integral between t0 and tf*
x=[(T2)Fx)/m]e-(t/T)+v0t

I am doing something wrong as my answer of 6192.301 m, is not correct
 
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  • #2
getty102 said:

Homework Statement


Find Δx
Given:
Fxe-(t/T)
v0=-41.2 m/s
tf=84.54 s
T=46 s
Fx=13.4 N
m=8.8 kg



Homework Equations


F=ma


The Attempt at a Solution


a=Fxe-(t/T)/m
dv/dt=Fxe-(t/T)/m

*integrate both sides*
v=[(-T)Fx)/m]e-(t/T)+v0
dx/dt=[(-T)Fx/m]e-(t/T)+v0

*take the definite integral between t0 and tf*
x=[(T2)Fx)/m]e-(t/T)+v0t

I am doing something wrong as my answer of 6192.301 m, is not correct

I think perhaps your problem comes in assuming that the constant of integration is equal to v0 (in red above). That is not the case in this situation. To see this, use the generic symbol "C" for the constant of integration here:[tex] v(t) = \int a(t)\,dt = \frac{F_x}{m}\int e^{-t/T}\,dt = -\frac{T F_x}{m} e^{-t/T} + C [/tex]Now, to solve for C, plug t = 0 into this expression. Note that e0 = 1, NOT 0:[tex] v(0) = v_0 = -\frac{T F_x}{m} + C \\ \Rightarrow C = v_0 + \frac{T F_x}{m}[/tex]If we plug this expression for C back into the expression for v(t), we end up with:[tex]v(t) = v_0 + \frac{T F_x}{m}(1 - e^{-t/T}) [/tex]Can you take it from here?
 

1. How is displacement related to force?

Displacement is directly proportional to force. This means that the greater the force applied, the greater the displacement will be.

2. What is the formula for finding displacement given force?

The formula for finding displacement given force is displacement = (force / mass) * time^2. This is based on Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

3. Can displacement be negative?

Yes, displacement can be negative. This indicates that the object has moved in the opposite direction of the applied force.

4. Can displacement be calculated with only the force value?

No, displacement cannot be calculated with only the force value. Other factors, such as mass and time, are needed to accurately calculate displacement using the formula mentioned above.

5. Is force the only factor that affects displacement?

No, there are other factors that can affect displacement, such as the mass of the object and the time period during which the force is applied. These factors must be taken into account when calculating displacement.

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