# An object with a mass of #6 kg# is hanging from a spring with a constant of #4 (kg)/s^2#. If the spring is stretched by #9 m#, what is the net force on the object?

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The net force on the object can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is ( F = -kx ), where ( F ) is the force exerted by the spring, ( k ) is the spring constant, and ( x ) is the displacement from the equilibrium position.

Given:

- Mass of the object, ( m = 6 ) kg
- Spring constant, ( k = 4 ) (kg)/s(^2)
- Displacement from equilibrium position, ( x = 9 ) m

Using Hooke's Law, we can find the force exerted by the spring:

[ F = -kx = -(4)(9) = -36 \text{ N} ]

Since the force exerted by the spring is opposite to the direction of displacement, we take it as negative.

To find the net force on the object, we also need to consider the force due to gravity. The force due to gravity can be calculated using the formula ( F = mg ), where ( m ) is the mass of the object and ( g ) is the acceleration due to gravity (( g \approx 9.8 ) m/s(^2) on Earth).

[ F = (6)(9.8) = 58.8 \text{ N} ]

The net force on the object is the vector sum of the forces due to the spring and gravity:

[ \text{Net force} = F_{\text{spring}} + F_{\text{gravity}} = -36 + 58.8 = 22.8 \text{ N} ]

So, the net force on the object is 22.8 N.

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The net force on the object is 36 N.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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