A 𝑚𝑟 = 550𝑘𝑔 rocket sled can be accelerated at a constant rate from rest to 𝑣𝑓 = 1500 𝑘𝑚ℎ𝑟 in𝑡𝑓 = 2𝑠 . What is the magnitude of the required net force? (3 sig. figs) (If the answer is greater
Question
A 𝑚𝑟 = 550𝑘𝑔 rocket sled can be accelerated at a constant rate from rest to 𝑣𝑓 = 1500 𝑘𝑚ℎ𝑟 in𝑡𝑓 = 2𝑠 . What is the magnitude of the required net force? (3 sig. figs) (If the answer is greater
Solution
First, we need to convert the final velocity from km/hr to m/s because the mass is given in kg and we want our force in Newtons (which is in kg*m/s²).
1 km/hr = 1000 m/3600 s = 0.27778 m/s
So, vf = 1500 km/hr = 1500 * 0.27778 m/s = 416.67 m/s
Next, we use the formula for acceleration which is final velocity minus initial velocity divided by time. Since the rocket starts from rest, the initial velocity is 0.
a = (vf - vi) / tf = (416.67 m/s - 0 m/s) / 2 s = 208.33 m/s²
Finally, we use the formula for force which is mass times acceleration.
F = m * a = 550 kg * 208.33 m/s² = 114583.33 N
So, the magnitude of the required net force is approximately 115,000 N (to 3 significant figures).
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