A person pulls a toboggan for a distance of 34.6 m along the snow with a rope directed 29.3 ° above the snow. The tension in the rope is 110 N. (a) How much work is done on the toboggan by the tension force? (b) How much work is done if the same tension is directed parallel to the snow?
Fap = 110N @ 29.3o. = Force applied.
Fp = 110*cos29.3 = 95.9 N. = Force parallel to the snow.
a. Work = Fp*d = 95.9 * 34.6 = 3319 J.
b. Work = 110 * 34.6 = 3806 J.
a) Well, let me calculate that for you. To find the work done on the toboggan, we can use the formula: work = force × distance × cos(theta), where theta is the angle between the force and the displacement. In this case, the force is 110 N, the distance is 34.6 m, and the angle is 29.3°. So, we have work = 110 N × 34.6 m × cos(29.3°). Now, let me get my calculator... *beep boop beep* The work done on the toboggan is approximately 3314.661 J.
b) If the tension is directed parallel to the snow, then the angle between the force and the displacement is 0°, since they are in the same direction. In this case, we have work = 110 N × 34.6 m × cos(0°). Now, we don't even need the calculator for this one! The work done is simply 110 N × 34.6 m × 1, which is equal to 3796 J.
So, the work done on the toboggan is 3314.661 J when the tension is directed at an angle, but increases to 3796 J when it's parallel to the snow. It seems like the toboggan prefers parallel tension, maybe it's more "snow-tisfying" for it!
To solve this problem, we need to use the equation for work:
Work = Force x Distance x cos(θ)
where:
- Work is the amount of work done,
- Force is the applied force,
- Distance is the displacement of the object, and
- θ is the angle between the force and the displacement vectors.
(a) How much work is done on the toboggan by the tension force?
Given:
- Distance = 34.6 m
- θ = 29.3°
- Force = 110 N
We need to find the work done by the tension force.
Using the equation for work:
Work = Force x Distance x cos(θ)
Plugging in the given values:
Work = 110 N x 34.6 m x cos(29.3°)
Calculating the value:
Work ≈ 3,548.45 J
Therefore, the work done on the toboggan by the tension force is approximately 3,548.45 Joules.
(b) How much work is done if the same tension is directed parallel to the snow?
In this case, the angle θ between the force and the displacement vectors is 0°, as the tension force is now directed parallel to the snow.
Using the equation for work again:
Work = Force x Distance x cos(θ)
Since cos(0°) = 1, we can simplify the equation:
Work = Force x Distance
Plugging in the given values:
Work = 110 N x 34.6 m
Calculating the value:
Work = 3806 N-m or 3806 J
Therefore, if the tension is directed parallel to the snow, the work done on the toboggan is 3806 Joules.
To find the work done on the toboggan by the tension force, we can use the formula:
Work = Force x Distance x cos(θ)
where:
- Work is the amount of work done
- Force is the applied force
- Distance is the distance covered by the object
- θ is the angle between the direction of the force and the direction of motion of the object
(a) Work done on the toboggan when the tension force is at an angle of 29.3° above the snow:
- Force = 110 N (given)
- Distance = 34.6 m (given)
- θ = 29.3° (given)
Substituting these values into the formula:
Work = 110 N x 34.6 m x cos(29.3°)
To evaluate this expression, we need to use the cosine function. If you don't have a calculator that supports trigonometric functions, you can use online calculators or smartphone apps that include scientific calculators.
Using a calculator, find the cosine of 29.3° and then multiply it by 110 N and 34.6 m to get the work done.
(b) Work done on the toboggan when the tension force is directed parallel to the snow:
In this case, the angle θ is 0° because the force and the direction of motion are parallel.
Applying the formula again:
Work = 110 N x 34.6 m x cos(0°)
The cosine of 0° is 1, so the formula simplifies to:
Work = 110 N x 34.6 m x 1
Evaluating this expression directly gives you the work done.
Remember to pay attention to the units when calculating work. The unit for work is Joules (J), and it is equal to N·m (Newton-meter).