A 2 kg mass moving at 8 m/s is subjected to a retarding force of -0.5 N. The mass will stop after traveling a distance of:
Understand the Problem
The question describes a mass moving with an initial velocity and subjected to a constant retarding force. We need to find the distance the mass travels before it comes to a stop. We can use the concepts of work, energy, and the work-energy theorem to solve this problem.
Answer
$5$ meters
Answer for screen readers
$5$ meters
Steps to Solve
- Calculate the initial kinetic energy
The initial kinetic energy ($KE$) of the mass is given by the formula: $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the initial velocity. $KE = \frac{1}{2} \times 2 \times (10)^2 = 100$ Joules.
- Calculate the work done by the retarding force
The work done ($W$) by the constant retarding force is given by $W = Fd$, where $F$ is the force and $d$ is the distance traveled. Since the force is retarding, the work done is negative with respect to the kinetic energy.
- Apply the work-energy theorem
The work-energy theorem states that the work done on an object equals the change in its kinetic energy. In this case, the final kinetic energy is zero since the mass comes to rest. Therefore, $W = \Delta KE = KE_{final} - KE_{initial} = 0 - 100 = -100$ Joules.
- Solve for the distance
We have $W = Fd$, so $-100 = -20 \times d$. Solving for $d$, we get $d = \frac{-100}{-20} = 5$ meters.
$5$ meters
More Information
The mass travels 5 meters before coming to rest under the influence of the retarding force.
Tips
A common mistake is not recognizing that the work done by the retarding force is negative, which directly opposes the motion and reduces the kinetic energy of the mass. Also, forgetting the work-energy theorem can lead to an incorrect approach.
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