A particular spring has a force constant of 2.6×103 .
Part A
How much mass would have to be suspended from the vertical spring to stretch it the first 5.6 ?
Express your answer using two significant figures.
How much more mass would have to be suspended from the vertical spring to stretch it the additional 3.0 ?
Express your answer using two significant figures.
I will be happy to check your thinking.
On the second part, look at the change in mass PE (m+M)gh=change in spring PE
(m+M)gh=1/2 k(5.6+3.0)^2-1/2 k (5.6^2)
solve for the additional mass m .
you did not include units for k, or distances, so they may need to be changed to be unit consistant.
To solve Part A, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement:
F = k * x
Where F is the force exerted by the spring, k is the force constant (also known as the spring constant), and x is the displacement of the spring.
In this case, the force constant is given as 2.6 × 10^3 N/m. We need to find the mass that would have to be suspended from the vertical spring to stretch it 5.6 cm (or 0.056 m).
Step 1: Rearrange Hooke's Law to solve for the force:
F = k * x
Step 2: Substitute the given values into the equation:
F = (2.6 × 10^3 N/m) * (0.056 m)
Step 3: Calculate the force:
F = 145.6 N
Step 4: Convert the force into mass:
F = m * g
where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Solve the equation for m:
m = F / g
m = 145.6 N / 9.8 m/s^2
Step 5: Calculate the mass:
m ≈ 15 kg (rounding to two significant figures)
Therefore, to stretch the spring by 5.6 cm, approximately 15 kg of mass needs to be suspended from it.
To solve the second part of the question, we need to find the additional mass required to stretch the spring by an additional 3.0 cm (or 0.03 m).
Step 1: Repeat Step 1 from Part A, rearranging Hooke's Law to solve for the force:
F = k * x
Step 2: Substitute the given values into the equation:
F = (2.6 × 10^3 N/m) * (0.03 m)
Step 3: Calculate the force:
F = 78 N
Step 4: Calculate the additional mass required:
m = F / g
m = 78 N / 9.8 m/s^2
Step 5: Calculate the mass:
m ≈ 8 kg (rounding to two significant figures)
Therefore, an additional mass of approximately 8 kg would have to be suspended from the vertical spring to stretch it by the additional 3.0 cm.