A small rocket weighs 14.7 newtons. The rocket is fired from a high platform but it's engine fails to burn properly. The rocket gains total upward force if only 10.2 newtons. At what rate and in what direction is the rocket accelerated?
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To find the rate and direction of acceleration for the rocket, we need to 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.
Given:
- Weight of the rocket = 14.7 N (downward force)
- Upward force gained = 10.2 N
First, we need to determine the net force acting on the rocket. The net force is the difference between the upward force gained and the weight of the rocket:
Net force = Upward force - Weight of the rocket
Net force = 10.2 N - 14.7 N
Net force = -4.5 N
The negative sign indicates that the net force is in the downward direction.
Next, we can calculate the acceleration of the rocket. We can rearrange Newton's second law of motion to solve for acceleration:
Acceleration = Net force / Mass
However, in this case, we don't have the mass of the rocket given. So, we will use the formula for weight to find the mass:
Weight = Mass * Acceleration due to gravity
Rearranging the formula for mass:
Mass = Weight / Acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2.
Mass = 14.7 N / 9.8 m/s^2
Mass ≈ 1.5 kg
Now we can calculate the acceleration:
Acceleration = Net force / Mass
Acceleration = -4.5 N / 1.5 kg
Acceleration ≈ -3 m/s^2
The acceleration of the rocket is approximately -3 m/s^2, in the downward direction.
To determine the rate and direction of acceleration for the rocket, we need to 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 (F = ma).
In this case, the net force acting on the rocket is 10.2 newtons, so we can write the equation as follows:
10.2 N = m * a
Since the weight of the rocket is given as 14.7 newtons, we know that the downward force acting on the rocket is 14.7 N. However, the upward force is only 10.2 N. Therefore, there is an overall downward force of 4.5 N acting on the rocket.
Using the equation F = ma, we can rearrange it to solve for acceleration:
a = F / m
Plugging in the values, we have:
a = 4.5 N / m
Now, we need to determine the mass of the rocket. Since weight is the force of gravity acting on an object, we can use the formula:
weight = mass * acceleration due to gravity (g)
In this case, the weight is 14.7 N and the acceleration due to gravity is approximately 9.8 m/s^2. We can rearrange the formula to solve for mass:
mass = weight / g
Substituting the values, we have:
mass = 14.7 N / 9.8 m/s^2
By calculating the value, we find that the mass of the rocket is approximately 1.5 kg.
Now, we can substitute the mass into the earlier equation for acceleration:
a = 4.5 N / 1.5 kg
Solving the equation, we find that the rocket is accelerated at a rate of 3 m/s^2 in the downward direction.