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Math  /  Algebra

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Learning Goal: To understand the meaning and possible applications of the work-energy theorem.
In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work-energy theorem. We will start with a special case: a particle of mass mm moving in the xx direction at constant acceleration aa. During a certain interval of time, the particle accelerates from viv_{\mathrm{i}} to vfv_{\mathrm{f}}, undergoing displacement ss given by s=xf−xis=x_{\mathrm{f}}-x_{\mathrm{i}}. a=vf2−vi22sa=\frac{v_{f}^{2}-v_{i}^{2}}{2 s}
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Part B
Find the net force FF acting on the particle. Express your answer in terms of mm and aa. View Available Hint(s)

Studdy Solution

STEP 1

1. We are dealing with a particle of mass m m moving in the x x -direction.
2. The particle is moving with constant acceleration a a .
3. The particle accelerates from an initial velocity vi v_i to a final velocity vf v_f .
4. The displacement of the particle is s=xf−xi s = x_f - x_i .
5. We need to find the net force F F acting on the particle.

STEP 2

1. Recall Newton's second law of motion.
2. Express the net force in terms of mass and acceleration.

STEP 3

Recall Newton's second law of motion, which states that the net force F F acting on an object is equal to the mass m m of the object multiplied by its acceleration a a .
F=m⋅a F = m \cdot a

STEP 4

Express the net force in terms of m m and a a .
Since we have already stated that F=m⋅a F = m \cdot a , this is the expression for the net force acting on the particle.
The net force F F is:
F=m⋅a F = m \cdot a

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