To bring his coconut to the market, a distance 15.0m from where he is, a vendor pushes his Carr by a force of 14.0N applied 30• with the horizontal. How much work did the vendor do?
work = force * distance = 14.0 cos 30° * 15.0 = _____ J
To find the work done by the vendor, we need to use the formula:
Work = Force × Distance × cos(θ)
where:
- Work is the amount of work done.
- Force is the applied force.
- Distance is the distance covered.
- θ is the angle between the direction of the force and the direction of motion.
In this case:
- Force = 14.0N
- Distance = 15.0m
- θ = 30°
First, we need to convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) × π/180
θ (in radians) = 30° × π/180
θ (in radians) = (π/6) radians
Now we can calculate the work done:
Work = 14.0N × 15.0m × cos(π/6)
Work = 14.0N × 15.0m × 0.866
Work ≈ 181.48 Joules
Therefore, the vendor did approximately 181.48 Joules of work.
To find the work done by the vendor in pushing the cart, we need to use the formula:
Work = Force * Distance * Cos(angle)
Here, we have:
Force = 14.0N
Distance = 15.0m
Angle = 30°
First, let's convert the angle from degrees to radians because the trigonometric functions in most programming languages use radians:
Angle in radians = Angle in degrees * (π/180)
Angle in radians = 30 * (π/180) = 0.5236 radians
Now, we can plug these values into the formula to calculate the work:
Work = 14.0N * 15.0m * Cos(0.5236 radians)
To find the cosine of 0.5236 radians, you can use a scientific calculator or lookup tables. Cos(0.5236) is approximately equal to 0.866.
Work = 14.0N * 15.0m * 0.866
Work ≈ 181.59 Joules
Therefore, the vendor did approximately 181.59 Joules of work in pushing the cart.