Melvin pulls a sled across level snow with a
force of 345 N along a rope that is 31◦
above
the horizontal.
If the sled moved a distance of 34.5 m, how
much work did Melvin do?
Cant be solved, unless something else is known, which is the acceleration the sled is undergoing. If it is not accelerating, then
work=345*cos31*distance
No you're good Bob. It can accelerate and the work will still be the same.
To find out how much work Melvin did, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where,
Force = 345 N (given)
Distance = 34.5 m (given)
θ = 31° (given)
Plugging in the values, we get:
Work = 345 N × 34.5 m × cos(31°)
Calculating the cosine of 31°:
cos(31°) ≈ 0.857
Now, substituting back into the equation:
Work ≈ 345 N × 34.5 m × 0.857
Calculating:
Work ≈ 10787.0175 J
Therefore, Melvin did approximately 10787.0175 Joules of work.
To find the work done by Melvin, we can use the formula:
Work = Force * Distance * cos(θ)
Where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the distance over which the force is applied (in meters, m)
- θ is the angle between the force and the direction of motion (in degrees)
In this case, we are given:
- Force = 345 N
- Distance = 34.5 m
- θ = 31°
We need to convert the angle from degrees to radians before we can use it in the formula. The conversion formula is:
radians = degrees * π / 180
θ_radians = 31° * π / 180 ≈ 0.5411 radians
Now, we can substitute the values into the formula:
Work = 345 N * 34.5 m * cos(0.5411 radians)
To calculate the cos(0.5411 radians), you can use a scientific calculator or an online calculator. The result will give us the amount of work done by Melvin.