A water skier, moving at a speed of 6.42 m/s, is being pulled by a tow rope that makes an angle of 39.7 ° with respect to the velocity of the boat (see the drawing). The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 131 N, determine the work that it does in 13.1 s.
Work=tension*distance*sinTheta
there theta is the angle between tension and the displacement vector (39.7deg)
distance=velocity*time
ARRRRGGGGG. Work=tension*distance*COSINETheta
sorry about that.
thanks
if your question is exactly like mine with velocity=8.06m/s, theta=38.3, Tension= 138N, and time is 14.5 the answer is 12656.92J ;)
To determine the work done by the tow rope, we can use the formula:
Work = Force × Distance × cos(θ)
where:
- Work is the amount of work done,
- Force is the magnitude of the force applied (in this case, the tension in the tow rope),
- Distance is the distance over which the force is applied,
- θ is the angle between the force and the displacement.
Given:
- Force = 131 N (tension in the tow rope)
- Distance = 13.1 s (time)
To find the distance, we can use the equation of motion:
Distance = Speed × Time
Given:
- Speed = 6.42 m/s
- Time = 13.1 s
Plugging the values into the equation, we have:
Distance = 6.42 m/s × 13.1 s
Calculating the value, we get:
Distance = 84.102 m
Now that we have the values of force (131 N), distance (84.102 m), and the angle (θ = 39.7°), we can plug them into the formula:
Work = 131 N × 84.102 m × cos(39.7°)
Evaluating this expression, we get:
Work = 10895.63 J
Therefore, the work done by the tow rope in 13.1 s is 10895.63 Joules.