A 18.4 kg block is dragged over a rough, horizontal
surface by a constant force of 126 N
acting at an angle of 34.1
◦
above the horizontal.
The block is displaced 20 m, and the
coefficient of kinetic friction is 0.123.
The acceleration of gravity is 9.8 m/s
2
.Find the work done by the force of friction.
Answer in units of J.
normal force down = 18.4*9.8 - 126 sin 34.1
so
friction force = .123 (18.4*9.8-126 sin 34.1)
work done by friction - friction force * 20 meters
To find the work done by the force of friction, we first need to calculate the frictional force acting on the block.
The frictional force can be obtained using the equation:
Frictional force = coefficient of kinetic friction * normal force
The normal force can be calculated using the equation:
Normal force = mass * acceleration due to gravity
Given:
- Mass of the block = 18.4 kg
- Coefficient of kinetic friction = 0.123
- Acceleration due to gravity = 9.8 m/s^2
Let's calculate the frictional force:
Normal force = 18.4 kg * 9.8 m/s^2
Normal force = 180.32 N
Frictional force = 0.123 * 180.32 N
Frictional force ≈ 22.20 N
Now we can calculate the work done by the force of friction:
Work = Force * displacement * cos(theta)
Given:
- Force = frictional force ≈ 22.20 N
- Displacement = 20 m
- Angle between the force and displacement = 34.1 degrees
Before we calculate the work, we need to convert the angle from degrees to radians:
theta (in radians) = 34.1 degrees * (π / 180)
theta (in radians) ≈ 0.595 radians
Now we can calculate the work done by the force of friction:
Work = 22.20 N * 20 m * cos(0.595 radians)
Work ≈ 413.26 J
Therefore, the work done by the force of friction is approximately 413.26 J.
To find the work done by the force of friction, we need to first calculate the frictional force acting on the block using the equation:
frictional force = coefficient of friction * normal force
The normal force is the force exerted by the surface on the block perpendicular to it, which is equal to the block's weight (mass * acceleration due to gravity):
normal force = mass * acceleration due to gravity = 18.4 kg * 9.8 m/s^2
Next, we need to find the frictional force:
frictional force = coefficient of friction * normal force
Next, we need to find the component of the applied force that acts parallel to the displacement. We can calculate it using the equation:
force parallel = applied force * cos(angle)
Now, we can calculate the work done by the force of friction using the equation:
work done by friction = frictional force * displacement
Finally, we can substitute the given values into the equation to get the answer in Joules (J).