A spring has stiffness of 100Nmm, the initial compression of the spring is 15mm, and it is then compressed to 65mm.
1Nmm = 0.001Nm
100Nmm = 100 X 0.001 = 0.1Nm
Comp.1 = 15 mm = 0.015m
Comp.2 = 65 mm = 0.065m
a) i-Find potential energy at 15mm.
ii- Find potential energy at 65mm.
The force exerted by the spring is:
at 15mm,Force=0.1X15
Force=1.5N
at 65mm,Force=0.1X65
Force=6.5N
Potential Energy(E_p )=Fd/2
E_p=1.5NX0.015m/2
E_p=0.01125Nm or 11.25mJ (Ans.to part a-i)
E_p2=(F_2 d_2)/2
E_p2=6.5NX0.065m/2
E_p2=0.21125Nm or 211.25mJ (Ans.to part a-i)
b) Find the work done during compression.
The average force applied between 15mm and 65mm= (1.5N+6.5N)/2=4N
Work Done=Fd
W.D.=4NX(0.065-0.015)m
W.D.=4X0.05
W.D.=0.2Nm or 20mJ (Ans.)
Repeat post. Already answered.
How come my work doesn't show up with my question??? Is it to long?
(-5)-(-3.4)=
To find the potential energy at 15mm, you need to first calculate the force exerted by the spring at that compression. The formula to calculate the force exerted by a spring is given by:
Force = stiffness * compression
In this case, the stiffness of the spring is 0.1Nm and the compression is 0.015m. Therefore:
Force = 0.1Nm * 0.015m
Force = 1.5N
Now that you have the force, you can calculate the potential energy using the formula:
Potential Energy = (Force * displacement) / 2
Plugging in the values:
Potential Energy = (1.5N * 0.015m) / 2
Potential Energy = 0.01125Nm or 11.25mJ
So, the potential energy at 15mm is 11.25mJ.
To find the potential energy at 65mm, you follow the same steps. The force at 65mm is calculated as:
Force = 0.1Nm * 0.065m
Force = 6.5N
Using the potential energy formula:
Potential Energy = (6.5N * 0.065m) / 2
Potential Energy = 0.21125Nm or 211.25mJ
So, the potential energy at 65mm is 211.25mJ.
To find the work done during compression, you need to calculate the average force applied between 15mm and 65mm. The average force is calculated as:
Average Force = (Force1 + Force2) / 2
Average Force = (1.5N + 6.5N) / 2
Average Force = 4N
Now you can use the formula for work done:
Work Done = Average Force * displacement
Plugging in the values:
Work Done = 4N * (0.065m - 0.015m)
Work Done = 4N * 0.05m
Work Done = 0.2Nm or 20mJ
So, the work done during compression is 20mJ.