A force acts for 5 seconds on a body of mass 5.2 kg initially at rest. The force then ceases to act and the body moves with a speed of 3m/s find magnitude of force
Not understood
final Ke = (1/2) m v^2 = (1/2)(5.2)(3)^2 = 23.4 Joules
work in = force * distance = F * d = 23.4
what is distance?
average speed = 3/2 = 1.5 m/s
d = 1.5 m/s * 5 s = 7.5 meters
so
F* 7.5 = 23.4
F = 23.4 / 7.5
Average speed is d/t not d*t
The answer is 78N
To find the magnitude of the force, we can use the equation that relates force, mass, and acceleration.
The initial velocity of the body is zero since it is initially at rest. The final velocity of the body is given as 3 m/s.
We can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Since u = 0, the equation becomes v = at.
The time taken for the force to act is given as 5 seconds.
Rearranging the equation, we have a = v/t.
Now, we know that the force is related to the acceleration by Newton's second law, which states that Force (F) equals mass (m) times acceleration (a): F = ma.
Plugging in the given values, we have:
m = 5.2 kg (mass)
v = 3 m/s (final velocity)
t = 5 s (time)
From the equation a = v/t, we can calculate the acceleration:
a = v/t = 3 m/s / 5 s = 0.6 m/s^2
Now, we can substitute the acceleration into Newton's second law:
F = ma = 5.2 kg * 0.6 m/s^2
Calculating the magnitude of force:
F = 3.12 Newtons
Therefore, the magnitude of the force acting on the body is 3.12 Newtons.