A spring with 50 N/m hangs vertically next to a ruler. The end of the spring is next to the 21-cm mark on the ruler.If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?

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To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

1. First, let's calculate the displacement of the spring when the 2.5-kg mass is attached. We can use the formula:

F = k * x

where F is the force, k is the spring constant, and x is the displacement.

Rearranging the formula, we have:

x = F / k

Substituting the values into the equation:

x = 50 N / 50 N/m = 1 m

So, the spring is displaced by 1 meter.

2. Next, let's convert the displacement to centimeters to determine where the end of the spring lines up with the ruler marks. Since 1 meter is equal to 100 centimeters, we can multiply the displacement by 100:

x = 1 m * 100 cm/m = 100 cm

Therefore, the end of the spring will line up with the 100-cm mark on the ruler.

To determine where the end of the spring will line up with the ruler marks when a 2.5-kg mass is attached, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

The formula for Hooke's Law is given by:

F = -kx

Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.

In this case, the spring constant is given as 50 N/m, and the displacement is the change in length of the spring. We need to determine the change in length of the spring when a 2.5-kg mass is attached.

To calculate the change in length, we can use the weight of the object, which is equal to the gravitational force acting on it. The gravitational force is given by:

F = mg

Where:
F is the force due to gravity,
m is the mass of the object,
and g is the acceleration due to gravity, which is approximately 9.8 m/s².

Substituting the values, we have:

F = (2.5 kg) * (9.8 m/s²) = 24.5 N

Now, we can solve for the displacement (change in length) using Hooke's Law:

F = -kx

24.5 N = - (50 N/m) * x

Solving for x:

x = (24.5 N) / (50 N/m) = 0.49 m

Since the spring is hanging vertically next to the ruler, the displacement represents the distance the spring will stretch downwards. Therefore, the end of the spring will line up with the ruler at a distance of 0.49 m below the 21-cm mark.

To find the final position of the end of the spring from the 21-cm mark, we subtract the displacement from the initial position:

Final position = 21 cm - 0.49 m = 21 cm - 49 cm = -28 cm

Therefore, the end of the spring will line up with the ruler at approximately -28 cm.

F = m * g = 2.5kg * 9.8N/kg = 24.5 N.

d = (24.5N/50N) * 1m = 0.49m. = 49 cm.

End of spring = 21 + 49 = 70 cm.