A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 65.6-kg water-skier has an initial speed of 5.2 m/s. Later, the speed increases to 11.9 m/s. Determine the work done by the net external force acting on the skier.
To determine the work done by the net external force acting on the skier, we first need to find the change in kinetic energy. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The equation for calculating kinetic energy is:
KE = (1/2)mv²
Where:
KE is the kinetic energy,
m is the mass of the object, and
v is the velocity of the object.
We can calculate the initial kinetic energy (KE1) and the final kinetic energy (KE2) using the given values:
KE1 = (1/2)m(5.2 m/s)²
KE2 = (1/2)m(11.9 m/s)²
Now, let's calculate the work done by the net external force using the formula:
Work = KE2 - KE1
Substituting the values we obtained:
Work = (1/2)m(11.9 m/s)² - (1/2)m(5.2 m/s)²
Work = (1/2)(65.6 kg)(11.9 m/s)² - (1/2)(65.6 kg)(5.2 m/s)²
Work = (1/2)(65.6 kg)(141.61 m²/s²) - (1/2)(65.6 kg)(27.04 m²/s²)
Now, we can simplify and calculate the result:
Work = (1/2)(65.6 kg)(141.61 m²/s² - 27.04 m²/s²)
Work = (1/2)(65.6 kg)(114.57 m²/s²)
Work ≈ 4,880.58 J
Therefore, the work done by the net external force acting on the skier is approximately 4,880.58 Joules.