A 279 N force is pulling an 75.9-kg refrigerator across a horizontal surface. The force acts at an angle of 26.3 ° above the surface. The coefficient of kinetic friction is 0.259, and the refrigerator moves a distance of 9.14 m. Find (a) the work done by the pulling force, and (b) the work done by the kinetic frictional force.
The work done by the pulling force is
A = F •s •cos α = 279•9.14•cos26.3° = 2286.1 Joules.
The work done by the kinetic frictional force is
Afr = Ffr •s •cos α =kmgscos180°=
=0.259•75.9•9,8•(-1)= - 195.6.
To find the work done by the pulling force and the work done by the kinetic frictional force, we first need to calculate the net force acting on the refrigerator.
Step 1: Calculate the vertical component of the pulling force.
The vertical component of the pulling force can be found using the formula:
F_vertical = F * sin(theta)
where F is the magnitude of the pulling force, and theta is the angle it makes with the horizontal surface.
Using the given values:
F = 279 N
theta = 26.3°
F_vertical = 279 N * sin(26.3°)
F_vertical ≈ 119.68 N
Step 2: Calculate the normal force.
The normal force is the force exerted by the surface perpendicular to the surface. In this case, the normal force is equal to the weight of the refrigerator.
The weight of the refrigerator can be calculated using the formula:
Weight = mass * gravitational acceleration
Using the given value:
mass = 75.9 kg
gravitational acceleration = 9.8 m/s^2
Weight = 75.9 kg * 9.8 m/s^2
Weight ≈ 743.82 N
Since the refrigerator is on a horizontal surface, the normal force (N) is equal to the weight of the refrigerator:
N = 743.82 N
Step 3: Calculate the frictional force.
The frictional force can be calculated using the formula:
Frictional force = coefficient of friction * normal force
Using the given value:
coefficient of kinetic friction = 0.259
Frictional force = 0.259 * 743.82 N
Frictional force ≈ 192.14 N
Step 4: Calculate the horizontal component of the pulling force.
The horizontal component of the pulling force can be found using the formula:
F_horizontal = F * cos(theta)
Using the given values:
F = 279 N
theta = 26.3°
F_horizontal = 279 N * cos(26.3°)
F_horizontal ≈ 250.07 N
Step 5: Calculate the net force.
The net force is the vector sum of the horizontal component of the pulling force and the frictional force.
Net force = F_horizontal - Frictional force
Net force = 250.07 N - 192.14 N
Net force ≈ 57.93 N
Step 6: Calculate the work done by the pulling force.
The work done by the pulling force can be calculated using the formula:
Work = force * displacement * cos(theta)
Using the given values:
force = 279 N
displacement = 9.14 m
theta = 26.3°
Work = 279 N * 9.14 m * cos(26.3°)
Work ≈ 2360.99 J
Therefore, the work done by the pulling force is approximately 2360.99 Joules.
Step 7: Calculate the work done by the kinetic frictional force.
The work done by the kinetic frictional force can be calculated using the formula:
Work = force * displacement * cos(180°)
Using the given values:
force = 192.14 N
displacement = 9.14 m
Work = 192.14 N * 9.14 m * cos(180°)
Work ≈ -1664.37 J
Therefore, the work done by the kinetic frictional force is approximately -1664.37 Joules.
In conclusion:
(a) The work done by the pulling force is approximately 2360.99 Joules.
(b) The work done by the kinetic frictional force is approximately -1664.37 Joules.
To find the work done by the pulling force, we can use the formula:
Work = force * distance * cos(angle),
where:
- Work is the amount of work done (in joules),
- Force is the magnitude of the pulling force (in newtons),
- Distance is the distance the refrigerator is pulled (in meters),
- Angle is the angle between the force and the direction of displacement.
(a) Work Done by the Pulling Force:
Given data:
Magnitude of the pulling force, Force = 279 N
Distance, Distance = 9.14 m
Angle, Angle = 26.3 °
Substituting these values into the formula, we have:
Work = 279 N * 9.14 m * cos(26.3 °)
Calculating:
Work = 279 N * 9.14 m * cos(0.4553)
Work ≈ 2508.27 J
Therefore, the work done by the pulling force is approximately 2508.27 joules.
(b) Work Done by the Kinetic Frictional Force:
To find the work done by the kinetic frictional force, we can use the formula:
Work = force of friction * distance,
where:
- Work is the amount of work done (in joules),
- Force of friction is the magnitude of the frictional force (in newtons),
- Distance is the distance the refrigerator is pulled (in meters).
The magnitude of the frictional force can be found using the equation:
Force of friction = coefficient of friction * normal force,
where:
- Coefficient of friction is given as 0.259, and
- Normal force can be calculated as the weight of the refrigerator, which is equal to mass * gravity.
First, let's calculate the normal force:
Mass of the refrigerator, Mass = 75.9 kg
Gravity, g = 9.8 m/s^2 (acceleration due to gravity)
Normal force = Mass * g
Normal force = 75.9 kg * 9.8 m/s^2
Calculating:
Normal force ≈ 743.82 N
Now, we can calculate the magnitude of the frictional force using the equation:
Force of friction = coefficient of friction * normal force
Force of friction = 0.259 * 743.82 N
Calculating:
Force of friction ≈ 192.40 N
Finally, to find the work done by the kinetic frictional force, we use the formula:
Work = force of friction * distance
Given data:
Force of friction = 192.40 N
Distance = 9.14 m
Substituting these values into the formula, we have:
Work = 192.40 N * 9.14 m
Calculating:
Work ≈ 1759.82 J
Therefore, the work done by the kinetic frictional force is approximately 1759.82 joules.