Question

A vertical spring stretches 3.9 cm when a 10−g object is hung from it. The object is replaced with a block of mass 25 g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

Answer 1

To calculate the period of motion for an object attached to a spring, we can use the equation T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant. The period is affected by changes in mass and spring constant.

Step-by-step explanation:

To calculate the period of motion, we can use the equation:

T = 2π√(m/k)

Where T is the period, m is the mass of the object, and k is the spring constant.

In this case, we need to find the mass of the block, which is given as 25g, or 0.025kg. The spring constant is not given, so we can't calculate the exact period without that information.

However, we can use the equation to understand how the period is affected by changes in mass and spring constant. When the mass is increased, the period will increase. And when the spring constant is increased, the period will decrease.

Answer 2

The period of the motion is approximately 0.996 seconds.

Step-by-step explanation:

To calculate the period of motion for an object attached to a vertical spring, we can use the equation:

T = 2π√(m/k) where T is the period, m is the mass of the object, and k is the spring constant.

In this case, the mass is 25 g (0.025 kg) and the spring constant can be determined using Hooke's law: F = kx, where F is the force applied to the spring and x is the displacement.

Since the object stretches the spring by 3.9 cm (0.039 m) and the force applied is the weight of the object (mg), we can determine k as follows: k = F/x = (0.025 kg * 9.8 m/s²) / 0.039 m = 6.33 N/m.

Now we can substitute the values in the equation: T = 2π√(0.025 kg / 6.33 N/m) ≈ 0.996 seconds.