A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.41 s, and the spring in the scale has a force constant of 640 N/m.

What is the mass of the grapes?
What is the weight of the grapes?

To find the mass of the grapes, we can use Hooke's Law, which relates the force exerted by the spring to the displacement of the object attached to it. The formula for Hooke's Law is:

F = k * x

where F is the force, k is the spring constant, and x is the displacement. In this case, the force is equal to the weight of the grapes.

To find the weight of the grapes, we can use the formula:

W = m * g

where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

To find the mass, we need to find the force and divide it by the acceleration due to gravity. However, we don't have the force directly, but we can find it using the period of oscillation.

The formula for the period of oscillation of a mass-spring system is:

T = 2π * sqrt(m / k)

where T is the period, m is the mass, and k is the spring constant.

From the given information, the period T is 0.41 s and the spring constant k is 640 N/m. We can rearrange the formula to solve for the mass:

m = (T^2 * k) / (4π^2)

Substituting the values:

m = (0.41^2 * 640) / (4π^2)

m ≈ 0.048 kg

Therefore, the mass of the grapes is approximately 0.048 kg.

To find the weight of the grapes, we can use the formula W = m * g:

W = 0.048 kg * 9.8 m/s^2

W ≈ 0.47 N

Therefore, the weight of the grapes is approximately 0.47 Newtons.