Question

this is a 2 part question42) A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.48 s, and the spring in the scale has a force constant of 650 N/m. What are (a) the mass and (b) the weight of the grapes?

Answer 1

The mass of the grapes is approximately 0.122 kg, calculated using the period of oscillation and the spring force constant. Their weight is approximately 1.20 N, derived from the mass and the acceleration due to gravity.

Step-by-step explanation:

To determine the mass of the grapes, we can use the formula of the period of a mass-spring system, T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the force constant of the spring. Given the period T = 0.48 s and the force constant k = 650 N/m, we can solve for m as follows:

T = 2π√(m/k)

0.48 = 2π√(m/650)

m = (0.48 / (2π))² × 650

m ≈ 0.122 kg

The weight of the grapes can then be calculated using the equation weight W = m × g, where g is the acceleration due to gravity (approximately 9.81 m/s²). Therefore, W = 0.122 kg × 9.81 m/s² ≈ 1.20 N.

(a) The mass of the grapes is approximately 0.122 kg.
(b) The weight of the grapes is approximately 1.20 N.

Answer 2

a) The diagram representing the scenario is shown below

The spring experiences ossilations. The number of ossilations is the period The formula for calculating the period is expressed as

T = 2 x pi x square root of (m/k)

where

T is the period

m is the mass of the grape

k is the spring constant

From the information given,

T = 0.48

k = 650

pi = 3.14

By substituting these values into the formula, we have

`\begin{gathered} 0.48\text{ = 2}*3.14*\sqrt[]{(m)/(650)} \\ \sqrt[]{(m)/(650)}\text{ = }(0.48)/(2*3.14)=\text{ 0.076} \\ \text{Squaring both sides of the equation, we have} \\ (m)/(650)=0.005776 \\ m\text{ = 650 }*0.005776 \\ m\text{ = }3.75 \end{gathered}`

The mass of the grape is 3.75kg

b) Weight = mass x acceleration due to gravity

If acceleration due to gravity = 10m/s^2,

Then

Weight = 3.75 x 10 = 37.5N