Hockey Puck A 110 g hockey puck sent sliding over ice is stopped in 13 m by the frictional force on it from the ice.
(a) If its initial speed is 5.0 m/s, what is the magnitude of the frictional force?
1 N
(b) What is the coefficient of friction between the puck and the ice?
2
Vf^1=Vi^2 + 2ad but a= force/mass, so
you can solve for force.
coefficent offriction:
frictionforce=mu*mg solve for mu.
you have to give formulas not answers
v = u + a*t
so t = (v-u)/a
x = t (v+u)/2
substituting for t, x = (v+u)(v-u)/2a
put in known values:
13 = (5)(-5)/2a
a = -25/26 m/s^2
f = m*a
u(k) * f(normal) = m*a
u(k) *m*g = m*a
u(k) = a/g
u(k) = -25/26 /9.81 = 0.098
where u(k) = coefficient of friction
for magnitude of friction force:
u(k)*m*g = 0.098 * 0.110kg * 9.81 m/s^2 = 0.106N
To find the magnitude of the frictional force and the coefficient of friction between the puck and the ice, we can use the principle of work done by friction.
(a) To find the magnitude of the frictional force, we can use the work-energy principle.
The work done by friction is given by the equation:
Work = Change in kinetic energy.
The initial kinetic energy of the puck is given by the equation:
Kinetic energy = 1/2 * mass * (initial velocity)^2.
The final kinetic energy of the puck is zero because it comes to a stop.
Therefore, we can calculate the work done by friction using the equation:
Work = Final kinetic energy - Initial kinetic energy.
Given:
Mass of the puck (m) = 110 g = 0.110 kg,
Initial velocity (v) = 5.0 m/s,
Distance over which the puck stops (d) = 13 m.
We can now calculate the work done by friction and find the magnitude of the frictional force.
Initial kinetic energy:
Initial kinetic energy = 1/2 * mass * (initial velocity)^2
= 1/2 * 0.110 kg * (5.0 m/s)^2
Final kinetic energy:
Final kinetic energy = 0
Work done by friction:
Work = Final kinetic energy - Initial kinetic energy
= 0 - [1/2 * 0.110 kg * (5.0 m/s)^2]
Since the work done by friction is equal to the magnitude of the frictional force multiplied by the distance (Work = Force * Distance), we can rearrange the equation to solve for the magnitude of the frictional force.
Force = Work / Distance
Force = [1/2 * 0.110 kg * (5.0 m/s)^2] / 13 m
Therefore, the magnitude of the frictional force is given by the equation above.
(b) To find the coefficient of friction between the puck and the ice, we need to use the equation:
Force of friction = Coefficient of friction * Normal force.
The normal force is equal to the weight of the puck (mg), where g is the acceleration due to gravity.
Therefore, we can rearrange the equation to solve for the coefficient of friction.
Coefficient of friction = Force of friction / Normal force
Coefficient of friction = [1/2 * 0.110 kg * (5.0 m/s)^2] / (0.110 kg * g)
To calculate the coefficient of friction, we need to know the acceleration due to gravity (g), which is approximately 9.8 m/s^2.
Substituting the values into the equation, we can calculate the coefficient of friction.