I will be happy to check your work. Break the puling force into horizontal and vertical components.
work= forcehorizontal*distance.
(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?
work= forcehorizontal*distance.
Work = Force * Displacement * cos(θ)
Where:
- Work represents the amount of work done on the object (in Joules).
- Force represents the applied force (in Newtons).
- Displacement represents the distance traveled by the object (in meters).
- θ represents the angle between the force and the displacement vectors (in degrees).
Let's calculate the work done in both scenarios:
(a) When the tension force is directed 25.0° above the snow:
- Force = 85.0 N (given)
- Displacement = 20.0 m (given)
- θ = 25.0° (given)
Work = 85.0 N * 20.0 m * cos(25.0°)
To calculate the cosine of 25.0°, we can use a scientific calculator or a mathematical software tool.
Work = 85.0 N * 20.0 m * 0.907
Work ≈ 1542 J
Therefore, the work done on the toboggan by the tension force when directed 25.0° above the snow is approximately 1542 Joules.
(b) When the tension force is directed parallel to the snow:
- Force = 85.0 N (given)
- Displacement = 20.0 m (given)
- θ = 0° (force is parallel to displacement)
Work = 85.0 N * 20.0 m * cos(0°)
Since the cosine of 0° is equal to 1,
Work = 85.0 N * 20.0 m * 1
Work = 85.0 N * 20.0 m
Work = 1700 J
Therefore, the work done on the toboggan by the tension force when directed parallel to the snow is 1700 Joules.