A rocket that weighs 7840 N on earth is fired. The force of propulsion is + 10 440N. Determine a) the mass of the rocket, b) the acceleration of the rocket, c) the velocity of the rocket at the end of 8.0 s.
m = 7840/9.81
10440 - 7840 = m a
v = a t = 8 a
a. 800
To solve the given problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. We can use this equation to find the mass and acceleration of the rocket.
a) Mass of the rocket:
The weight of the rocket on Earth is equal to the force acting on it due to gravity. Therefore:
Weight = mass × acceleration due to gravity
Given that the weight of the rocket is 7840 N, and the acceleration due to gravity is approximately 9.8 m/s², we can rearrange the equation to solve for the mass:
mass = Weight / acceleration due to gravity
mass = 7840 N / 9.8 m/s²
mass ≈ 800 kg
Therefore, the mass of the rocket is approximately 800 kg.
b) Acceleration of the rocket:
We can use Newton's second law of motion to find the acceleration of the rocket:
Force = mass × acceleration
The force of propulsion is given as +10,440 N, and the mass of the rocket is approximately 800 kg. Rearranging the equation gives:
acceleration = Force / mass
acceleration = 10,440 N / 800 kg
acceleration ≈ 13.05 m/s²
Therefore, the acceleration of the rocket is approximately 13.05 m/s².
c) Velocity of the rocket at the end of 8.0 s:
To find the velocity of the rocket at the end of 8.0 seconds, we can use the equation of motion:
final velocity = initial velocity + (acceleration × time)
Assuming the rocket starts from rest (initial velocity is 0 m/s), and the acceleration is constant at 13.05 m/s², we have:
final velocity = 0 m/s + (13.05 m/s² × 8.0 s)
final velocity ≈ 104.4 m/s
Therefore, the velocity of the rocket at the end of 8.0 seconds is approximately 104.4 m/s.
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
a) To find the mass of the rocket, we need to use the equation F = m * a. The force of propulsion is given as +10,440 N. When the rocket is on Earth, it also experiences a gravitational force of 7840 N acting downward (weight). However, in this case, we assume that the force of propulsion and the gravitational force are acting in the same direction. Therefore, the net force is the sum of these two forces: 10,440 N + 7840 N = 18,280 N.
Using Newton's second law, we can rearrange the equation to solve for mass: m = F / a.
Substituting the values, we have m = 18,280 N / a.
b) To find the acceleration of the rocket, we first need to convert the mass of the rocket to kilograms (since the SI unit for mass is kilograms). We can use the equation weight = mass * gravitational acceleration (w = m * g), where weight is given as 7840 N and gravitational acceleration on Earth is approximately 9.8 m/s^2. Rearranging the equation, we have m = weight / g = 7840 N / 9.8 m/s^2.
Substituting the value of mass into the equation m = 18,280 N / a, we have 7840 N / 9.8 m/s^2 = 18,280 N / a. Rearranging the equation to solve for acceleration, we get a = 18,280 N / (7840 N / 9.8 m/s^2).
c) To find the velocity of the rocket at the end of 8.0 s, we can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity (which can be assumed as zero since the rocket is initially at rest), a is the acceleration, and t is the time. Rearranging the equation, we have v = a * t.
Substituting the values of acceleration and time into the equation v = a * t, we have v = (18,280 N / (7840 N / 9.8 m/s^2)) * 8.0 s.
Simplifying the equation, we have v = 18,280 N / 7840 N * 9.8 m/s^2 * 8.0 s.
Calculate the values above to find the answers to parts a), b), and c).