The motor of a ski boat generates an average power of 7.30 104 W when the boat is moving at a constant speed of 10 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 8.40 104 W. What is the tension in the tow rope that is pulling the skier?
The difference in power required from the motor. 1.1*10^4 W, is the towing work, which equals rope tension times velocity. Solve for the tension.
To find the tension in the tow rope, we need to apply the concept of work and power.
When the boat is moving at a constant speed without pulling the skier, the power generated by the motor is given as 7.30 x 10^4 W.
The power generated by the motor when the boat is pulling the skier is given as 8.40 x 10^4 W.
The power generated by the motor can be calculated using the equation:
Power = Force x Velocity
Since the boat is moving at a constant speed, the power generated by the motor is equal to the tension in the tow rope multiplied by the boat's speed.
So, we can set up the following equations:
7.30 x 10^4 W = Tension x 10 m/s (Equation 1)
8.40 x 10^4 W = Tension x 10 m/s (Equation 2)
We can solve these equations simultaneously to find the tension (Tension) in the tow rope.
- Divide Equation 2 by Equation 1:
(8.40 x 10^4 W) / (7.30 x 10^4 W) = (Tension x 10 m/s) / (Tension x 10 m/s)
Simplifying,
1.1507 = 1
Since 1.1507 does not equal 1, it means that the tension (Tension) in the tow rope cannot be determined from the given information.
Therefore, the tension in the tow rope is unknown based on the given data.