Question

Consider a block on frictionless ice. Starting from rest, the block travels a distance din

time t when force Fis applied. If force 4F is applied, the distance the block travels in
time tis:

Answer 1

The distance is now 4d

Step-by-step explanation:

Mechanical Force

According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:

F = m.a

Where a is the acceleration of the object.

The acceleration can be calculated by solving for a:

`\displaystyle a=(F)/(m)`

Once we know the acceleration, we can calculate the distance traveled by the block as follows:

`\displaystyle d = vo.t+(at^2)/(2)`

If the block starts from rest, vo=0:

`\displaystyle d = (at^2)/(2)`

Substituting the value of the acceleration:

`\displaystyle d = ((F)/(m)t^2)/(2)`

Simplifying:

`\displaystyle d = (Ft^2)/(2m)`

When a force F'=4F is applied and assuming the mass is the same, the new acceleration is:

`\displaystyle a'=(4F)/(m)`

And the distance is now:

`\displaystyle d' = (4Ft^2)/(2m)`

Dividing d'/d:

`\displaystyle (d' )/(d)=((4Ft^2)/(2m))/((Ft^2)/(2m))`

Simplifying:

`\displaystyle (d' )/(d)=4`

Thus:

d' = 4d

The distance is now 4d