An object of mass 200.0kg is moving from rest under the influence of net force 1.0Kn.Find the acceleration of the object and work done within 20.0s. What is the velocity of the object ar the end of 20.0s interval of time?.Calculate the kinetic energy
F=ma solve for a.
Vf=Vi+at where a= F/Mass
To find the acceleration of the object, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The formula for acceleration is:
acceleration (a) = net force (F) / mass (m)
Given:
Net force (F) = 1.0 Kn (which is equivalent to 1000 N)
Mass (m) = 200.0 kg
Substituting these values into the formula, we get:
acceleration (a) = 1000 N / 200.0 kg
= 5 m/s^2
So, the acceleration of the object is 5 m/s^2.
To calculate the work done, we can use the formula:
work (W) = force (F) * distance (d)
Given:
Force (F) = 1.0 Kn (which is equivalent to 1000 N)
Distance (d) = unknown
To calculate the distance, we need to know the initial velocity of the object before the 20.0s interval of time. If the object was at rest initially, the initial velocity would be 0 m/s.
Using the formula for average velocity:
velocity (v) = initial velocity (u) + (acceleration (a) * time (t))
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 5 m/s^2
Time (t) = 20.0 s
Substituting these values into the formula for velocity, we get:
velocity (v) = 0 m/s + (5 m/s^2 * 20.0 s)
= 100 m/s
Now that we have the distance, we can calculate the work done:
work (W) = force (F) * distance (d)
= 1000 N * d
Given:
Work (W) = unknown
To calculate the work done, we need to know the distance traveled by the object within the 20.0s interval of time. If we assume the object's initial velocity was 0 m/s, we can use the formula for distance traveled under constant acceleration:
distance (d) = (initial velocity (u) * time (t)) + (0.5 * acceleration (a) * time (t)^2)
Substituting the given values into the formula:
distance (d) = (0 m/s * 20.0 s) + (0.5 * 5 m/s^2 * (20.0 s)^2)
= 0 m + (0.5 * 5 m/s^2 * 400.0 s^2)
= 0 m + (1000.0 m)
= 1000.0 m
Now we can calculate the work done:
work (W) = force (F) * distance (d)
= 1000 N * 1000.0 m
= 1,000,000 Nm
= 1,000,000 J (since 1 J = 1 Nm)
So, the work done within the 20.0s interval of time is 1,000,000 J (Joules).
Finally, to calculate the kinetic energy of the object, we can use the formula:
kinetic energy (KE) = 0.5 * mass (m) * velocity^2
Given:
Mass (m) = 200.0 kg
Velocity (v) = 100 m/s (which we calculated earlier)
Substituting these values into the formula, we get:
kinetic energy (KE) = 0.5 * 200.0 kg * (100 m/s)^2
= 0.5 * 200.0 kg * 10,000 m^2/s^2
= 1,000,000 J (Joules)
So, the kinetic energy of the object is 1,000,000 J (Joules).