1. A force of 720N stretches a certain spring a distance of 15 cm. What is its force constant? If a 60-kg mass is hung on it, how far will it stretch?
To find the force constant of the spring, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it stretches or compresses. Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the spring.
k is the force constant (also known as the spring constant).
x is the displacement of the spring from its equilibrium position.
In this case, we are given the force (F = 720 N) and the displacement (x = 15 cm = 0.15 m). We can rearrange the equation to solve for the force constant:
k = F / x
k = 720 N / 0.15 m
k = 4800 N/m
So, the force constant of the spring is 4800 N/m.
Now, let's determine how far the spring will stretch when a 60 kg mass is hung on it. We can use the equation:
F = mg
Where:
F is the force applied to the spring (which we know is 720 N).
m is the mass (60 kg).
g is the acceleration due to gravity (approximately 9.8 m/s²).
Rearranging the equation to solve for the force:
F = mg
720 N = 60 kg * 9.8 m/s²
The mass cancels out, and we can solve for g:
g = 720 N / 60 kg
g = 12 m/s²
Now, we can use Hooke's Law again to calculate the displacement:
F = k * x
720 N = 4800 N/m * x
Rearranging the equation to solve for x:
x = 720 N / 4800 N/m
x = 0.15 m
So, when a 60 kg mass is hung on the spring, it will stretch by 0.15 meters.