Question

Find the net force FnetFnetF_net acting on the sled. Express your answer in terms of some or all of the variables mmm, sss, v1v1v_1, and v2v2v_2.

Answer 1

Complete Question

The kinetic energy K of an object of mass m moving at a speed v is defined as . It seems reasonable to say that the speed of an object--and, therefore, its kinetic energy--can be changed by performing work on the object. In this problem, we will explore the mathematical relationship between the work done on an object and the change in the kinetic energy of that object.

Let us now consider the situation quantitatively. Let the mass of the sled be m and the magnitude of the net force acting on the sled be    The sled starts from rest.

Consider an interval of time during which the sled covers a distance s and the speed of the sled increases from v_1 to v_2. We will use this information to find the relationship between the work done by the net force (otherwise known as the net work) and the change in the kinetic energy of the sled.

Find the net force acting on the sled.

Express your answer in terms of some or all of the variables m,s,$v_1$, and v_2.

Answer:

The expression is  $F_{net} = \frac{1}{2s} * m * (v_2^2 - v_1^2)$

Explanation:

From the question we are told that

   The net force is $F_{net}$

    The  distance is  s

     The first velocity is  $v_1$

     The second velocity is  $v_2$

     The mass is  m

     

Generally the work energy theorem is mathematically represented as

       $W = F_{net} * s$

Also from the law energy conservation workdone is mathematically represented as

      $W = \Delta K$

Here  $\Delta K$ is the change in kinetic energy and this is mathematically represented as

      $\Delta K = \frac{1}{2} * m * \Delta v^2$

So

         $W = \frac{1}{2} * m * \Delta v^2$

Here  

      $\Delta v^2 = v^2_2 - v^2_1$

Hence

         $W = \frac{1}{2} * m * (v_2^2 - v_1^2)$

So

       $F_{net} * s = \frac{1}{2} * m * (v_2^2 - v_1^2)$

=>    $F_{net} = \frac{1}{2s} * m * (v_2^2 - v_1^2)$