You push your couch a distance of 3.6 m across the living room floor with a horizontal force of 198.0 N. The force of friction is 151.0 N. What is the work done by you, by the friction force, by gravity, and by the net force?
by you: 198*distance
by friction: 151*distance
by gravity: zilch
net force= force pushing-frictionforce
W=F.d , W= (198.0N)(3.6m)cos 0, W=712.8 N.m
this is your work.
W=(151.0N)(3.6)cos 180, W=(-1)543,6N.m
this work is negative because the force of friccion is opposite a the direction of movement y therefore the angle is 180
for last the total work is the sum of the all work
PS: the work of gravity is perpendicular
a the movement therefore cos 90 = 0.
Work gravity is 0
enjoy your answer.
To find the work done by different forces in this scenario, we can use the equation:
Work = Force × Distance × cos(θ)
Let's calculate the work done by each force individually:
1. Work done by you (applied force):
The horizontal force applied by you is 198.0 N, and the distance moved is 3.6 m. Since you applied the force horizontally, the angle (θ) between the force and the direction of motion is 0 degrees. Consequently, the cosine of 0 degrees is 1. Thus, the work done by you is:
Work = 198.0 N × 3.6 m × cos(0°) = 712.8 Joules
2. Work done by friction force:
The force of friction is given as 151.0 N, and the distance moved is still 3.6 m. The angle between the force of friction and the direction of motion is 180 degrees since friction opposes the motion. Therefore, the cosine of 180 degrees is -1. The work done by the friction force is:
Work = 151.0 N × 3.6 m × cos(180°) = -544.8 Joules (Note: The negative sign indicates that the work done by friction opposes the motion.)
3. Work done by gravity:
The problem statement does not mention any vertical motion or lifting, so we can assume that gravity does not perform any work in this scenario. The work done by gravity is zero.
4. Work done by the net force:
The net force is the vector sum of all the forces acting on the couch. In this case, it is the sum of the applied force and the force of friction. Since we are considering the horizontal motion only, the net force is:
Net Force = Applied Force - Force of Friction = 198.0 N - 151.0 N = 47.0 N
Therefore, the work done by the net force is:
Work = 47.0 N × 3.6 m × cos(0°) = 169.2 Joules
To summarize:
- Work done by you (applied force): 712.8 Joules
- Work done by friction force: -544.8 Joules
- Work done by gravity: 0 Joules
- Work done by net force: 169.2 Joules