The spring is fitted with a scale pan and the pointer points to the 30cm mark on the scale. When some sand is placed in the pan the pointer points to 15cn mark. When a 20g mass is placed on top of the sand the pointer points to 5cm mark.
a) what extension is produced by the sand?
b)what extension is produced by the mass of 20g mass?
c) what is the mass of the sand
a) The extension produced by the sand = 30cm - 15cm = 15cm
b) The extension produced by the 20g mass = 15cm - 5cm = 10cm
c) To calculate the mass of the sand, we need to first calculate the total extension produced by both the sand and the 20g mass:
Total extension = Extension produced by sand + Extension produced by mass
Total extension = 15cm + 10cm = 25cm
Now, we can use Hooke's Law to calculate the mass of the sand:
F = kx
Where F = force applied, k = spring constant, x = extension
Since we are dealing with mass here, we can convert the force to weight:
Weight = mass * gravity
Using the extension produced by the sand:
Weight of sand = k * 15cm * gravity
Weight of sand = 0.15kg * 9.81m/s^2
Weight of sand = 1.47N
Now, using the extension produced by the 20g mass:
Weight of 20g mass = 0.02kg * 9.81m/s^2
Weight of 20g mass = 0.1962N
Since the total weight on the scale is due to both the sand and the 20g mass:
Total weight on the scale = Weight of sand + Weight of 20g mass
Therefore, the mass of the sand can be calculated as:
Mass of the sand = (Total weight on the scale - Weight of 20g mass) / gravity
Mass of the sand = (1.47N - 0.1962N) / 9.81m/s^2
Mass of the sand = 0.128kg
So, the mass of the sand is 128g.