a body of mass 10kg is acted upon by a constant force of 30n,calculate the k.e gain by the body?
F = ma, so a = 3 m/s^2
the gain in KE will depend on how long the force acts, since
KE = 1/2 mv^2
and v = a*t
Lita,u
To calculate the kinetic energy gain by a body, you need to know the initial kinetic energy (K.E) and the final kinetic energy after the force is applied.
The formula for kinetic energy is:
K.E = (1/2) * mass * velocity^2
In this case, you are given the mass of the body (10 kg) and the force acting on it (30 N). To find the velocity, you can use Newton's second law of motion:
Force = mass * acceleration
Since the force is constant, you can rearrange the equation to find the acceleration:
acceleration = Force / mass
Substituting the given values, we have:
acceleration = 30 N / 10 kg = 3 m/s^2
Now, to find the velocity, you need to know the time for which the force acts. Let's assume the force acts for a duration of t seconds. Using the equation of motion:
velocity = initial velocity + acceleration * time
Since the body is initially at rest, the initial velocity is 0. Therefore:
velocity = 0 + 3 m/s^2 * t = 3t m/s
Now, substitute the velocity into the formula for kinetic energy:
K.E = (1/2) * mass * velocity^2
= (1/2) * 10 kg * (3t m/s)^2
= 45t^2 joules
So, the kinetic energy gain by the body is given by the expression 45t^2 joules. But to obtain a numerical value, you need to know the time for which the force acts.