You push your physics book 1.50 m along a horizontal tabletop with a horizontal force of 2.40N. The opposing force of friction is 0.60N.
a) how much work does your 2.40N force do on the book?
b) what is the work done on the book by the friction force?
c) what is the total work done on the book?
Work = Force exerted times distance in the direction of the force.
a) 2.4*1.5 J
b) -.6*1.5 J
c) difference
To calculate the work done on the book, we can use the formula:
Work = Force * Distance * cos(θ)
where:
- Work is measured in joules (J)
- Force is the applied force measured in newtons (N)
- Distance is the distance the object moves measured in meters (m)
- θ is the angle between the force vector and the direction of motion. In this case, since the force and displacement are both horizontal, the angle is 0° and therefore the cosine of 0° is 1.
a) To find the work done by the 2.40N force applied to the book, we can substitute the values into the formula:
Work = 2.40N * 1.50m * cos(0°)
Since cos(0°) = 1, the work done is:
Work = 2.40N * 1.50m * 1
Work = 3.60J
Therefore, the work done by the 2.40N force is 3.60 joules (J).
b) To find the work done by the friction force, we need to multiply the magnitude of the friction force by the distance moved:
Work = Friction Force * Distance * cos(θ)
Since the friction force is opposing the motion, the angle between the friction force and the displacement is 180°. The cosine of 180° is -1, so:
Work = 0.60N * 1.50m * cos(180°)
Work = 0.60N * 1.50m * -1
Work = -0.90J
Therefore, the work done by the friction force is -0.90 joules (J). The negative sign indicates that the work done by the friction force is in the opposite direction of motion.
c) To find the total work done on the book, we can sum up the work done by the applied force and the work done by the friction force:
Total Work = Work done by 2.40N force + Work done by friction force
Total Work = 3.60J + (-0.90J)
Total Work = 2.70J
Therefore, the total work done on the book is 2.70 joules (J).
To find the work done on the book, we can use the formula:
Work = Force × Distance × cosine(θ)
where
Work is the work done (in joules),
Force is the applied force (in newtons),
Distance is the distance over which the force is applied (in meters), and
θ is the angle between the force and the direction of motion.
In this case,
a) The force applied is 2.40 N, and the distance moved is 1.50 m. The angle between the force and the direction of motion is 0 degrees since they are both horizontal. Therefore,
Work = 2.40 N × 1.50 m × cosine(0)
= 2.40 N × 1.50 m × 1
= 3.60 joules
b) The force of friction is acting in the opposite direction to the applied force, so the angle between the friction force and the direction of motion is 180 degrees. Using the same formula,
Work (friction) = -0.60 N × 1.50 m × cosine(180)
= -0.60 N × 1.50 m × (-1)
= 0.90 joules (Note: The negative sign indicates that the work done by friction is in the opposite direction of the displacement)
c) The total work done on the book is simply the sum of the work done by the applied force and the work done by friction:
Total Work = Work (applied force) + Work (friction)
= 3.60 joules + 0.90 joules
= 4.50 joules
Therefore,
a) The force of 2.40 N does 3.60 joules of work on the book.
b) The friction force does 0.90 joules of work on the book.
c) The total work done on the book is 4.50 joules.