a block of ice initially sliding at 15m/s on a frozen pond comes to rest after traveling 90 meters. What is the coefficient of friction?
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To determine the coefficient of friction, we can use the formula:
frictional force = coefficient of friction * normal force
In this case, the frictional force is responsible for bringing the block of ice to rest. Initially, the block of ice was sliding with an initial velocity of 15 m/s and came to rest after traveling a distance of 90 meters.
Now, let's break down the problem step by step:
Step 1: Calculate the acceleration of the block of ice.
To determine the acceleration, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
u = initial velocity (15 m/s)
v = final velocity (0 m/s, as it comes to rest)
s = displacement (90 m)
Rearranging the equation, we have:
0 = 15^2 + 2a * 90
225 = 180a
a = 225/180
a = 1.25 m/s^2
Step 2: Calculate the normal force.
The normal force is the force exerted by the frozen pond on the block of ice and is equal in magnitude but opposite in direction to the gravitational force acting on it.
Since the block of ice is at rest, the normal force is equal to its weight (mass * gravitational acceleration).
Step 3: Calculate the frictional force.
The frictional force can be calculated using Newton's second law:
frictional force = mass * acceleration
And since we know that frictional force = coefficient of friction * normal force, we can rearrange the equation to solve for the coefficient of friction:
coefficient of friction = frictional force / normal force
Step 4: Plug in the values and calculate the coefficient of friction.
We need the mass of the block of ice to calculate the normal force. Since the mass is not given, we cannot directly determine the coefficient of friction without additional information.
Therefore, without knowing the mass of the block of ice, it is not possible to determine the coefficient of friction in this scenario.