A sled if pulled over level snow a distance of 0.500 km by a force of 124 n applied to a rope that makes an angle of 35.0 degrees with the snow. How much work is done?
124 cos 35 = 101.6 newtons is the force component along the direction of motion.
Multiply that by 500 m for the work done, in Joules
To find the work done, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
Force = 124 N (applied force)
Distance = 0.500 km = 500 m (distance covered by the sled)
theta = 35.0 degrees (angle between the applied force and the direction of motion)
First, let's convert the distance from kilometers to meters:
Distance = 0.500 km * 1000 m/km = 500 m
Now, we can calculate the work:
Work = 124 N * 500 m * cos(35.0 degrees)
To find the value of cos(35.0 degrees), we can use either a calculator or a trigonometric table.
Using a calculator:
cos(35.0 degrees) ≈ 0.8192
Work = 124 N * 500 m * 0.8192
Work ≈ 40,960 J
Therefore, the work done is approximately 40,960 J (Joules).
To calculate the work done in this scenario, we can use the formula:
Work = Force * Distance * cos(angle)
First, let's convert the given distance from kilometers to meters:
Distance = 0.500 km * 1000 m/km
Distance = 500 m
Now we can substitute the given values into the formula:
Work = 124 N * 500 m * cos(35.0 degrees)
However, remember that trigonometric functions in most programming languages and calculators use radians instead of degrees. So, we need to convert the angle from degrees to radians first:
Angle in radians = 35.0 degrees * pi/180 degrees
Angle in radians ≈ 0.610865 radians
Now we can substitute the values into the formula:
Work = 124 N * 500 m * cos(0.610865 radians)
Calculating the cosine of the angle, we get:
Work = 124 N * 500 m * 0.82534
Multiplying everything together, we obtain the work done:
Work ≈ 51,335 J (Joules)
Therefore, the work done to pull the sled over the level snow is approximately 51,335 Joules.