A traveler pulls on a suitcase strap at an angle 36 above the horizontal. If 555 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?
46 N
W=Fdcos(theta)
W=555J
d=15m
theta=36 degree
F=W/(dcos(theta))
F=555J/(15m*cos36)
F=46N
Work = Fap*Cos A * d = 555 J.
Fap*Cos36 * 15 = 555
12.14*Fap = 555
Fap = 45.7 N. = Force applied. = Tension
in the strap.
Well, let's calculate the tension in the strap using a touch of clown math!
First, let's find the angle in degrees that is "36 above the horizontal." If we add a clown twist to it, we get "36 above the horizontal...but never directly on it, because that would be too mainstream!" So, the angle is 36 degrees.
Now, to find the tension in the strap, we can use the clown formula:
Tension (T) = Work (W) / Distance (D) * Clown Angle (CA)
Plugging in the given values, we have:
T = 555 J / 15 m * 36 degrees
Calculating this clownishly complicated equation, we find that the tension in the strap is... drumroll please... **111 J/m**!
Wait, that's not right... Maybe I should've taken off my clown nose before doing the math. Let's try that again, shall we?
Using the proper equation, we have:
T = W / (D * cos CA)
Plugging in the values, we have:
T = 555 J / (15 m * cos 36 degrees)
After carefully crunching the numbers, it turns out that the correct tension in the strap is approximately **636.4 N**.
So, there you have it! The tension in the strap while pulling the suitcase at a clownish angle of 36 degrees above the horizontal is approximately 636.4 N. Happy travels!
To determine the tension in the strap, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its energy. In this case, the work done by the strap is equal to the change in the suitcase's kinetic energy.
The formula for work is given by:
Work = Force × Distance × cos(θ)
Where:
- Work is the energy transferred to the object (given as 555 J)
- Force is the magnitude of the force applied (tension in the strap)
- Distance is the magnitude of the displacement (given as 15 m)
- θ is the angle between the force and the displacement (given as 36 degrees above the horizontal)
Rearranging the formula, we can solve for the tension in the strap:
Tension = Work / (Distance × cos(θ))
Plugging in the values, we get:
Tension = 555 J / (15 m × cos(36°))
To calculate the tension, we need to convert the angle from degrees to radians:
Tension = 555 J / (15 m × cos(0.628)) (where 0.628 is the value of 36 degrees in radians)
Evaluated further:
Tension = 555 J / (15 m × 0.812)
Tension ≈ 48.33 N
Therefore, the tension in the strap is approximately 48.33 Newtons.