a force of 9.0N is applied to a body at rest on a smooyh horizontal surface. if the body has a mass of 18.0kg and it moves in the direction of the force, find the work done in; (a) the first four second (b) the fourth second.
What is the acceleration? Force = mass * acceleration; thus, acceleration = force/mass = 9N/18 kg = ½ meters/second^2
we also know that distance-traveled = initial displacement + time * initialVelocity + (acceleration * time^2)/2
because initial displacement = 0, and initialVelocity = 0, then distance-traveled = (acceleration * time^2)/2 = (½ * 4^2)/2 = 4 meters
Then Work = Force * distance = 9 N * 4 meters = 36 Newton meters
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www.quora.com/A-force-of-9-0-newtons-is-applied-to-a-body-at-rest-on-a-smooth-horizontal-surface-If-the-body-has-a-mass-of-18-0-kg-and-it-moves-in-the-direction-of-the-force-what-is-the-work-done-in-4-seconds
To find the work done, we need to use the formula:
Work (W) = Force (F) * Distance (d) * Cos(θ)
However, in this case, the body is moving on a smooth horizontal surface without any mention of the distance or angle of the force. Therefore, we can assume that the force is acting parallel to the direction of motion, making the angle (θ) between the force and displacement 0 degrees (Cos(0) = 1).
Let's calculate the work done in the different scenarios:
(a) First Four Seconds:
To calculate the work done in the first four seconds, we need to know the distance traveled by the body.
Using Newton's second law of motion: F = ma
Where F = 9.0 N (force) and m = 18.0 kg (mass)
We can calculate the acceleration (a):
9.0 N = 18.0 kg * a
a = 9.0 N / 18.0 kg = 0.5 m/s^2
To find the distance (d) traveled, we can use the formula of motion:
d = ut + (1/2) * a * t^2
Where u = 0 m/s (initial velocity), a = 0.5 m/s^2 (acceleration), t = 4 s (time)
d = 0 * 4 + (1/2) * 0.5 * (4)^2
d = 0 + (1/2) * 0.5 * 16
d = 4 meters
Now we can calculate the work done:
W = F * d * Cos(θ)
W = 9.0 N * 4 m * 1
W = 36 Joules
Therefore, the work done in the first four seconds is 36 Joules.
(b) Fourth Second:
To calculate the work done in the fourth second, we need to know the distance traveled in that specific time.
Using the same formulas as above, we know that the distance traveled in the first four seconds is 4 meters. Thus, we can deduce that the distance traveled in the first three seconds is 3 meters.
To find the distance traveled in the fourth second, we can subtract the distance traveled in the first three seconds from the total distance traveled in the first four seconds:
Distance traveled in the fourth second = Total distance - Distance traveled in the first three seconds
Distance traveled in the fourth second = 4 meters - 3 meters
Distance traveled in the fourth second = 1 meter
Now we can calculate the work done:
W = F * d * Cos(θ)
W = 9.0 N * 1 m * 1
W = 9 Joules
Therefore, the work done in the fourth second is 9 Joules.