A ski patroller pulls a rescue toboggan across a flat snow surface by exerting a force of 45 pounds on a handle that makes an angle of 22° with the horizontal. Find the work done in pulling the toboggan 160 feet.
Work= force*distance
= 45cos22*160 feet
= 6,675.72 N/Ft.
Why did the ski patroller become a workaholic? Because he's always pulling a toboggan uphill! But let's calculate the work done to confirm his efforts.
To find the work done, we can use the formula:
Work = Force × Distance × cos(θ)
Given:
Force (F) = 45 pounds
Distance (d) = 160 feet
Angle (θ) = 22°
Plugging the values into the formula, we have:
Work = 45 pounds × 160 feet × cos(22°)
Calculating this, we find that the work done in pulling the toboggan is approximately 5,698.69 foot-pounds.
Now the ski patroller can take a break and enjoy some downhill skiing!
To find the work done in pulling the toboggan, we need to calculate the dot product of the force and displacement vectors. The dot product is given by the formula:
Work = Force * Displacement * cos(theta)
Where:
Force = 45 pounds
Displacement = 160 feet
theta = 22°
Let's calculate the work done:
1. Convert the force to Newtons (since work is typically calculated in SI units):
1 pound = 0.45359 kilograms (approx.)
Force (in Newtons) = 45 pounds * 0.45359 kg/pound * 9.81 m/s^2 (approx.)
Force = 197.66 Newtons (approx.)
2. Convert displacement to meters (since force was converted to Newtons):
1 foot = 0.3048 meters (approx.)
Displacement (in meters) = 160 feet * 0.3048 meters/foot (approx.)
Displacement = 48.768 meters (approx.)
3. Convert theta from degrees to radians:
Theta (in radians) = 22° * (pi/180°)
Theta = 0.383972 radians (approx.)
4. Calculate the work done:
Work = force * displacement * cos(theta)
Work = 197.66 N * 48.768 m * cos(0.383972)
Work = 9382.84 Joules (approx.)
Therefore, the work done in pulling the toboggan 160 feet is approximately 9382.84 Joules.
To find the work done in pulling the toboggan, we can use the formula:
Work = Force × Distance × cos(angle)
First, let's convert the force from pounds to pounds-force. Since 1 pound-force is equal to the force of gravity (32.2 ft/s^2) on a mass of 1 pound, we have:
Force = 45 pounds × 32.2 ft/s^2
Next, let's convert the angle from degrees to radians:
Angle = 22° × π/180
Now we're ready to calculate the work:
Work = (45 pounds × 32.2 ft/s^2) × (160 feet) × cos(22° × π/180)
Using a calculator, we can evaluate this expression:
Work ≈ 11,160.28 foot-pounds
Therefore, the work done in pulling the toboggan 160 feet is approximately 11,160.28 foot-pounds.