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

To find the net force Fnet acting on a sled, apply Newton's Second Law of Motion using the formula Fnet = m (v2 - v1) / s, where m is mass, v1 is initial velocity, v2 is final velocity, and s is the time interval.

Step-by-step explanation:

The student is asking how to find the net force (Fnet) acting on a sled. The key to solving this problem is to apply Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (Fnet = ma). Since the acceleration can be derived from the change in velocity over time (a = (v2 - v1)/s), we can express the net force in terms of the given variables. Therefore, the net force on the sled is Fnet = m (v2 - v1) / s, where m represents the mass of the sled, v1 is the initial velocity, v2 is the final velocity, and s is the time taken for this change in velocity to occur.

Answer 2

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)   = (1)/(2s)  * m *  (v_2^2 -  v_1^2)`

Step-by-step 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 = (1)/(2) * m * \Delta v^2`

So

`W  =  (1)/(2)  * m *  \Delta v^2`

Here

`\Delta v^2  =  v^2_2 - v^2_1`

Hence

`W  =  (1)/(2)  * m *  (v_2^2 -  v_1^2)`

So

`F_(net) *  s  = (1)/(2)  * m *  (v_2^2 -  v_1^2)`

=>
`F_(net)   = (1)/(2s)  * m *  (v_2^2 -  v_1^2)`