find the initial velocity when givin the coefficient of friction and distance?

Question

A hockey player hits a puck giving it an initial velocity. The puck stops when it has traveled 20 meters. Along the way the puck was acted upon a friction coefficient of .2. What is the initial velocity? The question does not give a mass for the puck which isn't necessary for this problem. And my professor likes us to use the force as gravity as g=10m/s^2 (he likes rounding numbers).

scott8148 · Answer

the initial kinetic energy of the puck equals the work done by friction in stopping the puck

1/2 * m * v^2 = .2 * m * g * 20

cancelling the mass and multiplying by 2 ___ v^2 = 8 * g

jcherry_99 · Answer

Good for him. Rounding makes it possible to estimate.

Frictional forces can be written as Ff = u*N. The normal is the opposite force to the gravitational force

N = m*g

So the frictional force is 0.2 * m* g where g is 10 m/s^2

d = 20 meters
vf = 0 m/s
vi = ? This is what you are looking for.
a = ?

vf^2 = vi^2 + 2*a*d

The initial force is F = m*a
a = (vf^2 - vi^2 )/ (2*d)

so m * (vf^2 - vi^2)/(2*d) = m * g * 0.2 The m's cancel

Rearrange the formula so you are finding vi^2

2 * 2* 20 = vf^2 - vi^2
Friction is a negative force
- 80 = - vi^2
vi = sqrt(80)
vi = 4 sqrt(5).

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find the initial velocity when givin the coefficient of friction and distance?

2 Answers