Mass of a Body Accelerated by a Force

To calculate the mass of a body that is accelerated by a force, 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. The formula for this is:

F = ma

Where:
F = Force applied on the body (in Newtons)
m = Mass of the body (in kilograms)
a = Acceleration of the body (in meters per second squared)

In this case, we are given that a force of 200N is applied to a body, and it speeds up to 36 m/s. We need to find the mass of the body.

Step 1: Write down the given values
- Force (F) = 200N
- Final velocity (v) = 36 m/s

Step 2: Calculate the acceleration
Acceleration (a) can be calculated using the formula:

a = (v - u) / t

Where:
u = Initial velocity (assumed to be zero in this case)
t = Time taken to reach the final velocity

Since the initial velocity is assumed to be zero, the formula simplifies to:

a = v / t

In this case, the time is not given, so we cannot calculate the exact acceleration. However, we can proceed by assuming a value for time, which will allow us to find the mass.

Step 3: Assume a value for time
Let's assume that the time taken to reach the final velocity of 36 m/s is 4 seconds. This is just an arbitrary value used for calculation purposes.

Step 4: Calculate the acceleration using the assumed time
Using the assumed time of 4 seconds, we can calculate the acceleration:

a = v / t
a = 36 m/s / 4 s
a = 9 m/s^2

Step 5: Calculate the mass
Now that we have the force (200N) and the acceleration (9 m/s^2), we can use Newton's second law to calculate the mass:

F = ma
200N = m * 9 m/s^2

Solving for m:

m = 200N / 9 m/s^2
m ≈ 22.22 kg

Therefore, the mass of the body is approximately 22.22 kg.

Summary:
- Given force: 200N
- Final velocity: 36 m/s
- Assumed time: 4 seconds
- Calculated acceleration: 9 m/s^2
- Calculated mass: approximately 22.22 kg