131k views
0 votes
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:

User Morgane
by
7.3k points

1 Answer

4 votes

Answer:

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

User Fabian Zeindl
by
6.8k points