Work done by a constant force is defined as the product of the force applied and the displacement of the object in the direction of the force. Mathematically, it is expressed as W=F⋅d⋅cos(θ), where W is the work done, F is the magnitude of the constant force, d is the displacement, and θ is the angle between the force and the direction of displacement. When the force is applied in the same direction as the displacement, θ is 0 degrees, and the work done is maximized. Conversely, if the force is applied perpendicular to the displacement, no work is done. This concept is fundamental in physics as it relates to energy transfer and the efficiency of mechanical systems.
What is the formula for calculating work done by a constant force?
The formula is W=F⋅d⋅cos(θ), where W is work done, F is the force applied, d is the displacement, and θ is the angle between the force and
If a force of 10 N is applied to move an object 5 meters in the direction of the force, what is the work done?
The work done is W = 10N ⋅ 5m ⋅ cos(0o) = 50J.
What happens to the work done if the angle between the force and displacement is 90 degrees?
If the angle is 90 degrees, cos(90∘)=0, so the work done is zero, meaning no work is done when the force is perpendicular to the displacement.
How does the direction of the force affect the work done?
The direction of the force affects the work done through the cosine of the angle between the force and the displacement; work is maximized when the force is in the same direction as the displacement and minimized (to zero) when perpendicular.
Can work be done if an object does not move?
No, if there is no displacement, the work done is zero, regardless of the amount of force applied.
What is the formula for work done by a constant force?
a) W = F⋅d
b) W = F⋅d⋅sin(θ)
c) W = F⋅d⋅cos(θ)
d) W = F+d
Answer: c) W = F⋅d⋅cos(θ)
If a force of 50 N is applied at an angle of 0 degrees to the direction of motion and the object moves 10 meters, what is the work done?
a) 0 J
b) 50 J
c) 500 J
d) 1000 J
Answer: c) 500 J
When is the work done by a force zero?
a) When the force is applied
b) When the object moves
c) When the force is perpendicular to the displacement
d) When the object is at rest
Answer: c) When the force is perpendicular to the displacement
What is the SI unit of work?
a) Newton
b) Joule
c) Watt
d) Meter
Answer: b) Joule
If a constant force of 30 N is applied to move an object 5 meters at an angle of 60 degrees to the direction of motion, what is the work done?
a) 75 J
b) 150 J
c) 130 J
d) 90 J
Answer: a) 75 J