A 826 g rocket, initially at rest, lifts vertically off the launching pad reaching a velocity of 373 m/s in 7.9 seconds. To the nearest tenth of a Newton, how much thrust (a type of force) acts to produce the rocket's motion?
To find the amount of thrust acting on the rocket, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a):
F = m * a
In this case, the mass of the rocket is given as 826 g. To use this in the equation, we need to convert it to kilograms, since the standard unit for mass is kg. 1 kg is equal to 1000 g, so the mass of the rocket in kilograms is:
m = 826 g / 1000 = 0.826 kg
The acceleration of the rocket can be calculated using the formula:
a = (v - u) / t
Where v is the final velocity, u is the initial velocity, and t is the time taken. Plugging in the given values:
v = 373 m/s
u = 0 m/s (since the rocket starts from rest)
t = 7.9 s
a = (373 m/s - 0 m/s) / 7.9 s = 47.15 m/s^2 (rounded to two decimal places)
Now, we can substitute the values of mass (m = 0.826 kg) and acceleration (a = 47.15 m/s^2) into the equation for force (F = m * a):
F = 0.826 kg * 47.15 m/s^2
Calculating this multiplication gives us:
F = 38.67 N
Therefore, to the nearest tenth of a Newton, the amount of thrust acting on the rocket is approximately 38.7 N.