Question

How much force do you need to accelerate a 2kg mass at 4 m/s^2

Answer 1

Answer:

8N

Explanation:

According to the given question,

m = mass = 2 kg

a = acceleration = 4 m/s^2

F = force

And we are asked to find the force.

We know, from Newton's 2nd law,

• F = ma

Putting the values we get,

• F = 2×4

• F = 8 N

Thus force produced is 8N when mass of the body is 2kg and it's acceleration is 4 m/s^2.

Answer 2

$\huge \mathfrak{The\ force\ produced\ by\ the\ body\ is\ 8N.}$

Explanation:

What is force?

Any push or pull on a body, which can make it stop or move is called a force.

In this case we've to move (accelerate) a body of mass 2 kg at a velocity of $\rm 4 m/s^2.\\ \rm So,\ the\ formula\ to\ find\ force\ of\ the\ body\ is\ F=m×a\\ \rm Putting\ values\\ \rm F= 2\times 4 \\ \implies \rm F=8\\ \therefore \bf The\ Force\ produced\ by\ the\ body\ is\ 8\ N$

$\rm \huge \underline{Proof\ that\ F=m\times a}$

According to Newton's 2nd law of motion: The rate of change of momentum of a body is directly proportional to the applies force, and takes place in the direction in which the force acts.

$\rm So,\ this\ can\ be\ written\ as\ \bf Force\propto \frac{Change\ in\ momentum}{Time\ taken}$

Now, consider a body of mass m having an initial velocity u. The initial velocity of this body will be mu. Suppose a force F acts on this body for time t and causes the final velocity to become v. The final momentum of this body will be mv. Now the change in momentum of this body is mv-mu and the time taken for this change is t.

$\sf So,\ according\ to\ Newton's\ second\ law\ of\ motion: F\propto \frac{mv-mu}{t} -(1)\\ \\ \implies F\propto \frac{m(v-u)}{t}\\ \\ or F\propto m\times \frac{v-u}{t}\\ \\ \sf And\ we\ know\ that\ \frac{v-u}{t}=a\\ \\ \therefore \sf we'll\ put\ a\ instead\ of\ \frac{v-u}{t} in\ equation\ (1)\\ \\ \therefore \sf F\propto m\times a\\ Putting\ a\ constant\ k,\ we\ get\ F=m\times a\times k$

Know, that

F= force {SI unit newton (N)}

m= mass {SI unit kilogram (Kg.)}

a= acceleration {SI unit is mass by square of time (m/s^2)}

The value of constant k is 1 in SI unit, so this can be given as F=m×a.