Russell drags his suitcase 15.0 M from the door of his house to the car at a constant speed with a horizontal force of 95.0 N. H
1 answer:
The work done is 1425 J
Explanation:
The work done by a force to move an object is given by
where
F is the magnitude of the force
d is the displacement
is the angle between the direction of the force and of the displacement
For the suitcase in this problem, we have:
F = 95.0 N is the force applied
d = 15.0 m is the displacement
, since the force is parallel to the displacement
Substituting, we find
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- Magnitude: 12.1 N.
- Direction: 17.0° to the 8 N force.
Refer to the diagram attached (created with GeoGebra). Consider the 5 N force in two directions: parallel to the 8 N force and normal to the 8 N force.
.
.
The sum of forces on each direction will be the resultant force on that direction:
- Resultant force parallel to the 8 N force:
.
- Resultant force normal to the 8 N force:
.
Apply the Pythagorean Theorem to find the magnitude of the resultant force.
(3 sig. fig.).
The size of the angle between the resultant force and the 8 N force can be found from the tangent value of the angle. Tangent of the angle:
.
Find the size of the angle using inverse tangent:
.
In other words, the resultant force is 17.0° relative to the 8 N force.
