A 0.6-kg object moves in a horizontal circular track with a radius of 3.3m. An external force of 6.8 N, always tangent to the track , causes the object to speed up as it goes around. The work done by the external force as the object makes one revolution is equal to what value in Joule?
force * distance in direction of the force = work done by force = 6.8 N * 2 pi * 3.3 meters = 141 Joules
To find the work done by the external force, we can use the formula:
Work = Force * Distance * cos(theta)
where:
- Force is the magnitude of the external force
- Distance is the distance over which the force is applied
- theta is the angle between the force and the distance
In this case, the force is tangent to the circular track, so the angle theta is 90 degrees (or pi/2 radians).
The distance over which the force is applied is equal to the circumference of the circular track, which can be calculated using the formula:
Circumference = 2 * pi * radius
Let's calculate the work done:
Force = 6.8 N
Radius = 3.3 m
Circumference = 2 * pi * 3.3m
= 2 * 3.14 * 3.3m
= 20.73m (approximately)
Now we can calculate the work done:
Work = Force * Distance * cos(theta)
= 6.8 N * 20.73m * cos(90 degrees)
= 6.8 N * 20.73m * 0
= 0
Therefore, the work done by the external force as the object makes one revolution is equal to 0 Joules.
To find the work done by the external force as the object makes one revolution, we need to use the formula for work:
Work = Force * Distance * cos(θ)
In this case, the force (F) is given as 6.8 N, and the distance (d) is equal to the circumference of the circular track, which can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the circular track. In this case, the radius is given as 3.3 m, so:
Circumference = 2 * π * 3.3
To find the angle (θ) between the force and the displacement, we can note that the force is always tangent to the track, which means it is perpendicular to the displacement. Therefore, the angle between the force and the displacement is 90 degrees. Since cos(90°) = 0, the cos(θ) term in the formula becomes 0.
Now we can plug in the values into the formula for work:
Work = 6.8 N * (2 * π * 3.3 m) * cos(90°)
Since cos(90°) = 0, the work done by the external force as the object makes one revolution is:
Work = 6.8 N * (2 * π * 3.3 m) * 0
Since anything multiplied by 0 is 0, the work done by the external force is 0 Joule.