How to Calculate the Speed of a Wagon Moving Up a Hill?
What is the scenario of the problem given?
A 38.2 kg wagon is towed up a hill inclined at 17.5 ◦ with respect to the horizontal. The tow rope is parallel to the incline and has a tension of 129 N in it. Assume that the wagon starts from rest at the bottom of the hill, and neglect friction. The acceleration of gravity is 9.8 m/s 2. How fast is the wagon going after moving 85.4 m up the hill?
Calculation of Speed:
Given data:
Mass (m) = 38.2 kg
Inclined angle (θ) = 17.5°
Towing force (Ft) = 129 N
Distance moved (d) = 85.4 m
Acceleration due to gravity (g) = 9.8 m/s^2
Explanation:
As the wagon is pulled up by a string system, the net force acting on the wagon along the inclined plane is due to tension in the rope and the component of weight along the inclined plane.
Using the work-energy theorem, we can calculate the speed of the wagon:
Ft * d - (m * g * sin(θ) * d) = (1/2) * m * v^2 - 0
After substituting the given values into the equation and solving for v, we find:
Speed (v) = 8.57 m/s
To calculate the speed of a wagon moving up a hill, we need to consider the forces acting on the wagon and apply the work-energy theorem. In this scenario, the tension in the rope and the gravitational force are the main factors influencing the motion of the wagon.
By using the given mass, towing force, inclined angle, distance moved, and acceleration due to gravity, we can set up an equation that relates the work done by these forces to the change in kinetic energy of the wagon.
After solving the equation, we find that the speed of the wagon is 8.57 m/s after moving 85.4 m up the hill. This calculation helps us understand the relationship between forces, work, and kinetic energy in the context of moving objects on inclined planes.