A 38.2 kg wagon is towed up a hill inclined at 19° with respect to the horizontal. The tow rope is parallel to the incline and exerts a force of 140 N on the wagon. Assume that the wagon starts from rest at the bottom of the hill, and disregard friction.How fast is the wagon going after moving 80.0 m up the hill?
Subtract the potential energy change from the work done. The difference wil be the final kinetic energy. Use that to get V.
To determine the speed of the wagon after moving 80.0 m up the hill, we need to use the concept of work and energy. Here's how you can calculate it:
1. Find the work done on the wagon by the force parallel to the incline.
- Work done (W) is calculated using the formula: W = force × distance × cos(theta), where theta is the angle between the force and the direction of motion.
- In this case, the distance is 80.0 m, the force is 140 N (parallel to the incline), and theta is the angle of the incline, which is 19°. Therefore:
W = 140 N × 80.0 m × cos(19°)
2. Calculate the change in potential energy (ΔPE) of the wagon as it moves up the hill.
- The change in potential energy is given by the formula: ΔPE = m × g × h, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the vertical height gained.
- In this case, h can be calculated by multiplying the distance by the sine of the angle: h = 80.0 m × sin(19°).
- Therefore, ΔPE = 38.2 kg × 9.8 m/s² × [80.0 m × sin(19°)]
3. Equate the work done to the change in potential energy and solve for the final velocity (v).
- The work done is equal to the change in potential energy: W = ΔPE.
- Therefore, 140 N × 80.0 m × cos(19°) = 38.2 kg × 9.8 m/s² × [80.0 m × sin(19°)].
4. Solve the equation for v.
- Rearrange the equation to solve for v: v = sqrt(2 × ΔPE / m).
- Inserting the values, we have: v = sqrt(2 × (38.2 kg × 9.8 m/s² × [80.0 m × sin(19°)]) / 38.2 kg).
5. Calculate the final velocity using the equation.
- Perform the numerical calculation to obtain the final velocity.
By following these steps, you should be able to calculate the final velocity of the wagon after moving 80.0 m up the hill.