A 10 N toy rocket is fired straight up [KE= 40 J]. At the very top of its trip, the total mechanical energy= 140 J. What was the final maximum height reached?
When I tried to solve the problem, I got 10 m for the answer. Can anyone tell me whether or not that's the right answer?
To determine the final maximum height reached by the toy rocket, we can use the principle of conservation of mechanical energy. The total mechanical energy, which includes both kinetic energy (KE) and potential energy (PE), remains constant throughout the rocket's motion.
Given:
Initial kinetic energy (KE) = 40 J
Total mechanical energy at the top (PE + KE) = 140 J
Let's break down the problem and solve it step by step:
Step 1: Determine the initial potential energy (PE) at the launchpad.
Since the toy rocket is fired straight up, we can assume it starts from the ground, where the potential energy is zero. Therefore, the initial potential energy is zero.
Step 2: Calculate the initial total mechanical energy (TME_initial).
TME_initial = PE_initial + KE_initial = 0 + 40 J = 40 J
Step 3: Calculate the final potential energy (PE_final) at the top of the rocket's trip.
PE_final = TME_final - KE_final
Given:
Total mechanical energy at the top (TME_final) = 140 J
Final kinetic energy (KE_final) = 0 (at the very top, the velocity is zero)
PE_final = 140 J - 0 J = 140 J
Step 4: Determine the change in potential energy (ΔPE) from the launchpad to the top.
ΔPE = PE_final - PE_initial = 140 J - 0 J = 140 J
Step 5: Calculate the final maximum height (h) using the change in potential energy.
PE = m * g * h
Given:
Force of gravity (g) = 10 N (acceleration due to gravity)
Change in potential energy (ΔPE) = 140 J
ΔPE = m * g * h
h = ΔPE / (m * g)
= 140 J / (10 N * 10 m/s²) [Considering 1 N = 1 kg * m/s²]
= 1.4 m
Therefore, the final maximum height reached by the toy rocket is 1.4 meters.
If you obtained an answer of 10 meters, it seems there may have been an error in the calculations or assumptions made. Please double-check your work and ensure you have correctly followed the steps outlined above.