A net force of 47.0 N acts on a 53.0 kg body initially at rest. Compute the work (in joules) done by the force in the first second of time.
Not sure where to start at all :(
work = force * distance
so, how far does it travel in 1 second?
F=ma, so a=F/m
s = 1/2 at^2 = 1/2 (F/m) t^2
To find the work done by a force, you need to multiply the magnitude of the force by the displacement of the object in the direction of the force. However, in this case, you are not given the displacement directly. Instead, you need to calculate the displacement using the given information.
First, let's use Newton's second law of motion to find the acceleration of the body. The formula is:
F = m * a
where:
F is the net force (47.0 N),
m is the mass of the object (53.0 kg), and
a is the acceleration.
Rearranging the formula, we get:
a = F / m
Substituting the given values:
a = 47.0 N / 53.0 kg
Now, calculate the acceleration.
a ≈ 0.8868 m/s²
The initial velocity of the body is 0 m/s because it is initially at rest.
To find the displacement, we can use the kinematic equation:
v = u + a * t
where:
v is the final velocity (which we assume is v = u + a * t because the body starts from rest),
u is the initial velocity (0 m/s),
a is the acceleration (0.8868 m/s²), and
t is the time (1 second).
Simplify the equation to find the displacement:
v = a * t
s = u * t + (1/2) * a * t²
Substituting the given values:
s = 0 * 1 + (1/2) * 0.8868 * (1)²
Now, calculate the displacement.
s ≈ 0.4434 meters
Finally, we can calculate the work done by the force using the formula:
work = force * displacement
Substituting the given values:
work = 47.0 N * 0.4434 m
Now, calculate the work done.
work ≈ 20.85 joules
Therefore, the work done by the force in the first second of time is approximately 20.85 joules.