A skier is coasting on perfectt smooth snow at 7.0 m/s and crosses a rough patch of snow 35m long. If the frictional force exerted on the skier is 6.0 N, what is her speed as she leaves the patch of snow? Assume the skier and her skis habe a mass of 90.0 kg.
To find the skier's speed as she leaves the patch of snow, we can apply the conservation of energy principle. The initial kinetic energy will be equal to the final kinetic energy minus the work done by the frictional force.
The initial kinetic energy is given by:
KE_initial = (1/2) * mass * velocity_initial^2
Substituting the values:
KE_initial = (1/2) * 90.0 kg * (7.0 m/s)^2
= 2205 J
Now, let's calculate the work done by the frictional force. Work is defined as the force applied through a distance:
Work = force * distance
Substituting the values:
Work = 6.0 N * 35 m
= 210 J
Since the work done by the frictional force is negative (opposite to the direction of motion), we will subtract it from the initial kinetic energy.
KE_final = KE_initial - Work
= 2205 J - 210 J
= 1995 J
Finally, we can solve for the final velocity using the equation for kinetic energy:
KE_final = (1/2) * mass * velocity_final^2
Rearranging the equation:
velocity_final^2 = (2 * KE_final) / mass
Substituting the values:
velocity_final^2 = (2 * 1995 J) / (90.0 kg)
= 44.33 m^2/s^2
Taking the square root of both sides:
velocity_final = √(44.33 m^2/s^2)
= 6.66 m/s
Therefore, the skier's speed as she leaves the patch of snow is approximately 6.66 m/s.
friction work= 6N*35M=210joules.
finalKE= initialKE-210
1/2 m vf^2=1/2 m vi^2-210
Vf^2= vi^2-2*210
vi= 7 m/s