Question

A spring scale that reads in grams uses a 10.0-cm-long spring. Hanging a water bottle from the scale stretches the spring to 11.5 cm and causes the scale to read 350 g.

Answer 1

A spring scale measures weight based on the compression or extension of a spring. It provides a reading in grams or newtons, depending on the scale. The scale would measure the same 'mass' on Earth as on the Moon because mass is an intrinsic property of an object and does not change based on location.

A spring scale measures weight based on the compression or extension of a spring. When you hang an object from the scale, the weight of the object causes the spring to stretch. The scale reads the amount of stretch in the spring and provides a reading in grams or newtons, depending on the scale. In this case, the 10.0-cm-long spring stretched to 11.5 cm, indicating a weight of 350 grams. The scale is calibrated to provide information about the mass of a body.

To calculate the force constant of the spring, we can use Hooke's Law: F = kx, where F is the force, k is the force constant, and x is the displacement of the spring. In this case, the displacement is given as 1.5 cm, which is equivalent to 0.015 meters. The force constant can be calculated as 350 grams (converted to kilograms) divided by 0.015 meters, which gives a value of 23,333.33 N/m.

The scale would measure the same 'mass' on Earth as on the Moon because mass is an intrinsic property of an object and does not change based on location.

Answer 2

To determine the spring constant of the scale, you can use the formula:

k = (F / x)

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

In this case, the force acting on the spring is the weight of the water bottle, which can be calculated using the weight = mass * gravitational acceleration formula:

F = m * g

where m is the mass of the water bottle in kilograms and g is the gravitational acceleration of 9.8 m/s^2.

Plugging in the values given, we get:

k = (F / x) = (m * g / x)

= (350 g / (11.5 cm - 10.0 cm))

= 307.8 g/cm

This is the spring constant of the scale. It represents the force required to stretch the spring by 1 centimeter.