Question

A sled of mass m is given a kick on a frozen pond. The kick imparts to it an initial speed of 3.00 m/s. The coefficient of kinetic friction between sled and ice is 0.150. Use energy considerations to find the distance the sled moves before it stops.

Answer 1

Answer:

The distance moved by the sled before stopping is 3.06 m.

Explanation:

Given:

Mass of sled = 'm'

Initial speed of the sled (u) = 3.00 m/s

Final speed of the sled (v) = 0 m/s

Coefficient of friction between sled and ice (μ) = 0.150

Now, the velocity of the sled is decreasing with time. This means energy is lost in overcoming friction. Therefore, the energy change of the sled is equal to the work done by the frictional force.

The frictional force acting on the sled is given as:

$f=\mu N=\mu mg$

Where, $N=mg$ as there is no vertical motion.

Now, work done by friction is given as:

$W_f=-fd=-\mu mg d$

The negative sign implies friction and displacement are in opposite direction.

Now, from work energy theorem, the work done by net force is equal to the change in kinetic energy of the sled. This gives,

$\Delta K=W_f\\\\\frac{1}{2}m(v^2-u^2)=-\mu mgd\\\\d=\frac{v^2-u^2}{-2\mu g}$

Now, plug in the values given and solve for 'd'. This gives,

$d=\frac{0-(3.00)^2}{-2\times 0.150\times 9.8}\\\\d=\frac{9}{2.94}\\\\d=3.06\ m$

Therefore, the distance moved by the sled before stopping is 3.06 m.