Respuesta :
Answer:
a) 0.0693 m
b) Work done = 8.644 J
Explanation:
Given:
Spring constant, k = 3600 N/m
Radius of the piston, r = 0.028 m
Now, we know that the atmospheric pressure at STP = 1.01325 × 10⁵ Pa = 101325 Pa
Now,
The force ([tex]F_P[/tex]) due to the atmospheric pressure on the piston will be:
[tex]F_P[/tex] = Pressure × Area of the piston
on substituting the values we get,
[tex]F_P[/tex] = 101325 × πr²
F = 101325 × π × (0.028)² = 249.56 N
also,
Force on spring is given as:
F = kx
where,
x is the displacement in the spring
on substituting the values we get,
249.56 N = 3600N/m × x
or
x = 0.0693 m
thus, the compression in the spring will be = 0.0693 m
b) Applying the concept of conservation of energy
we have,
Work done by the atmospheric pressure in compressing the spring = Potential energy gained by the spring
mathematically,
[tex]W = \frac{1}{2}kx^2[/tex]
on substituting the values we get,
[tex]W = \frac{1}{2}\times 3600\times (0.0693)^2[/tex]
W = 8.644 J
a) x = 0.0693 m
b) W = 8.644 J
Given :
Spring constant, K = 3600 N/m
Radius of the piston, r = 0.028 m
Solution :
Now the atmospheric pressure at STP = 1.01325 × 10⁵ Pa = 101325 Pa
Force due to the atmospheric pressure on the piston is,
Force = Pressure × Area of the piston
on substituting the values we get,
[tex]\rm F_P = 101325\times \pi r^2[/tex]
[tex]\rm F_P = 249.56\;N[/tex]
a) We know that the force on spring is given by,
F = Kx
where, k is spring constant and x is the displacement in the spring.
[tex]249.56 = 3600\times x[/tex]
[tex]\rm x = 0.0693\;m[/tex]
b) We know that the Work Done is given by,
[tex]\rm W= \dfrac{1}{2} k x^2[/tex]
[tex]\rm W = 0.5\times 3600\times (0.0693)^2[/tex]
W = 8.644 J
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