assume that a 50 kg skater on level ice has built up her speed to 30km/hr.how far will she coast before the sliding friction dissipates her energy?
assume the friction coefficient is 0.01.
Waxan donaayaa jawabah
I am gonna answer
The solution
To determine how far the skater will coast before the sliding friction dissipates her energy, we need to calculate the force of sliding friction and use it to calculate the distance.
First, let's calculate the force of sliding friction. The formula for the force of sliding friction is given by:
Force of sliding friction = coefficient of sliding friction * normal force
The normal force can be calculated as the product of the mass (50 kg) and the acceleration due to gravity (9.8 m/s²):
Normal force = mass * acceleration due to gravity
Normal force = 50 kg * 9.8 m/s²
Next, substitute the coefficient of sliding friction (0.01) into the formula to calculate the force of sliding friction:
Force of sliding friction = 0.01 * normal force
Now we have the force of sliding friction. To find the distance the skater will coast, we can use the work-energy principle, which states that the work done on an object equals the change in its kinetic energy. In this case, the work done by the force of sliding friction will be dissipated as kinetic energy until the skater comes to a stop.
The work done by the force of sliding friction can be calculated as:
Work = force of sliding friction * distance
Since the work done by the force of sliding friction is dissipated as kinetic energy, it can be calculated as the change in kinetic energy:
Work = change in kinetic energy
The change in kinetic energy can be calculated as the initial kinetic energy (½ * mass * velocity²) minus the final kinetic energy (0 since the skater comes to a stop).
Now, let's calculate the initial kinetic energy:
Initial kinetic energy = ½ * mass * velocity²
Initial kinetic energy = ½ * 50 kg * (30 km/hr)^2
Before we can proceed, we need to convert the velocity from kilometers per hour to meters per second:
30 km/hr = 30,000 m/3,600 s
Now, let's calculate the initial kinetic energy:
Initial kinetic energy = ½ * 50 kg * (30,000 m/3,600 s)²
Finally, calculate the distance using the work-energy principle:
Work = change in kinetic energy
Force of sliding friction * distance = ½ * 50 kg * (30,000 m/3,600 s)²
Now, solve for distance:
distance = (½ * 50 kg * (30,000 m/3,600 s)²) / (force of sliding friction)
Plug in the values for mass, velocity, and the force of sliding friction to calculate the distance.