A hockey puck is given an initial speed of
30 m/s on a frozen pond. The puck remains
on the ice and slides 130 m before coming to
rest.
The acceleration of gravity is 9.8 m/s^2 .
What is the coefficient of friction between
the puck and the ice?
x = (v+u)(v-u)/2a
where x = distance, v = final speed, u = initial speed, a = acceleration
substituting known values:
130 = (30)*(-30)/2a
a = -900/260 = -3.46 m/s^2
f = ma
u(k)*f(normal) = m*a
u(k)*m*g = m*a
u(k) = a/g
u(k) = 3.46/9.8 = 0.35
blumeor
To calculate the coefficient of friction between the puck and the ice, we need to use the equations of motion. The first step is to find the deceleration of the puck.
We can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 m/s as the puck comes to rest)
u = initial velocity (30 m/s)
a = acceleration (deceleration in this case)
s = distance (130 m)
Rearranging the equation gives:
a = (v^2 - u^2) / (2s)
Substituting the values in:
a = (0^2 - 30^2) / (2 * 130)
a = (-900) / 260
a = -3.4615 m/s^2
The negative sign indicates that the acceleration is opposite to the initial velocity, as it's a deceleration.
Next, we can calculate the net force acting on the puck using the equation:
Fnet = m * a
Where:
m = mass of the puck
Since we are not provided with the mass of the puck, we can cancel out the mass by dividing both sides of the equation by m:
Fnet / m = a
The net force acting on the puck is the force of friction:
Ffriction = Fnet = m * a
Now we have all the information we need to calculate the coefficient of friction. The formula for friction force is:
Ffriction = friction coefficient * normal force
Where:
friction coefficient = coefficient of friction
normal force = force perpendicular to the surface (in this case, the weight of the puck)
The weight of the puck can be calculated using the formula:
Weight = m * g
Where:
g = acceleration due to gravity (9.8 m/s^2)
Rearranging the equation:
m = Weight / g
Substituting the values:
m = (Ffriction) / g
Now we can substitute the expression for m in terms of Ffriction into the equation for Ffriction:
Ffriction = (Ffriction) / g * a
Simplifying the equation:
1 = (Ffriction / g) * a
Now we can solve for the coefficient of friction:
friction coefficient = Ffriction / (m * g)
Substituting the value of m:
friction coefficient = (Ffriction / ((Ffriction / g) * g))
Simplifying further:
friction coefficient = Ffriction / Ffriction
Therefore, the coefficient of friction between the puck and the ice is 1.
To find the coefficient of friction between the puck and the ice, you need to use the concept of kinematics.
Here's how you can solve this problem step by step:
Step 1: Identify the relevant information:
- Initial speed of the puck (u) = 30 m/s
- Distance traveled by the puck (s) = 130 m
- Acceleration due to gravity (g) = 9.8 m/s^2
Step 2: Determine the final velocity of the puck.
The puck comes to rest, so the final velocity (v) is zero.
Step 3: Use the equation of motion to find the acceleration (a):
You can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Since the final velocity is zero, the equation becomes 0 = 30^2 + 2a(130).
Simplifying the equation, you get:
0 = 900 + 260a.
Step 4: Solve for the acceleration (a):
Rearrange the equation to isolate the acceleration:
260a = -900.
Divide both sides of the equation by 260:
a = -900/260.
Simplifying the division, you get:
a = -3.46 m/s^2.
Step 5: Calculate the frictional force (F_friction):
The frictional force can be calculated using the equation F_friction = m * a, where F_friction is the frictional force, m is the mass, and a is the acceleration.
Since the mass of the puck is not given, you can cancel it out by dividing both sides of the equation by m:
F_friction/m = a.
Step 6: Calculate the coefficient of friction (μ):
The coefficient of friction (μ) can be calculated using the equation μ = F_friction / (m * g), where μ is the coefficient of friction, F_friction is the frictional force, m is the mass, and g is the acceleration due to gravity.
By substituting the value of F_friction/m in terms of acceleration (from Step 5) into the equation, you get:
μ = (F_friction/m) / g.
Since F_friction/m = a (from Step 5), the equation becomes:
μ = a / g.
Step 7: Plug in the values and calculate:
Substitute the acceleration value you found in Step 4 and the acceleration due to gravity into the equation:
μ = (-3.46 m/s^2) / (9.8 m/s^2).
Calculating this division:
μ ≈ -0.35.
Therefore, the coefficient of friction between the puck and the ice is approximately -0.35.