Question

A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of v. The coefficient of kinetic friction between sled and ice is μk. Use energy considerations to find the distance the sled moves before it stops. (Use any variable or symbol stated above along with the following as necessary: g.)

Answer 1

The distance the sled moves before it stops can be found using conservation of energy. We can set the work done by friction equal to the initial kinetic energy to solve for the distance. The formula for the distance is d = (1/2) * (m * v^2) / (μk * m * g).

Step-by-step explanation:

To find the distance the sled moves before it stops, we can use conservation of energy. At the beginning, the sled has kinetic energy, which is given by the equation KE = (1/2)mv^2, where m is the mass of the sled and v is the initial speed. As the sled slides, it experiences friction, which dissipates its kinetic energy. The work done by friction is equal to the force of friction multiplied by the distance. The force of friction is given by the equation F_friction = μk * m * g, where μk is the coefficient of kinetic friction and g is the acceleration due to gravity. Setting the work done by friction equal to the initial kinetic energy and solving for the distance, we have d = (1/2) * (m * v^2) / (μk * m * g).

Answer 2

d = v² / (2μ g)

Step-by-step explanation:

In the work relationship is equal to the variation of energy,

W = ΔEm

The work is defined by

W = F. d ​​= F d cos θ

In this case the outside is the force of friction, which always opposes

to the movement, so the angle is 180 °

W = - fr d

The force of friction can be found with Newton's second law

fr = μ N

Y Axis

N- W = 0

N = mg

fr = μ m g

We substitute in the expression of work

W = - μ mg d

Now we use the relationship of work and energy

-μ mg d = 0 -½ m v²

d = v² / (2μ g)