The magnitude of the force on the mass due to the spring is 19.5 N.
Step-by-step explanation:
To find the magnitude of the force on the mass due to the spring, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Hooke's Law can be expressed as:
F = kx
Where F is the magnitude of the force, k is the force constant of the spring, and x is the displacement of the spring. In this case, we are given that the mass extends the spring by 1.33 m, so the displacement is -1.33 m (negative because the spring is stretched). We can rearrange the equation to solve for the force:
F = kx
F = (k)(-1.33)
Now we need to find the force constant, k. Hooke's Law can be rearranged to solve for k:
k = F/x
We are given the mass of the object, which is 2 kg. The force on the object due to gravity is given by the equation F = mg, where m is the mass and g is the acceleration due to gravity. Plugging in the values, we get:
F = (2 kg)(9.8 m/s^2)
Now we can substitute the values into the equation for k:
k = (19.6 N)/(1.33 m)
Simplifying, we get:
k = 14.7 N/m
Finally, we can substitute the values of k and x into the equation for F:
F = (14.7 N/m)(-1.33 m)
Simplifying, we get:
F = -19.5 N
Therefore, the magnitude of the force on the mass due to the spring is 19.5 N.