A loaded sled is pulled by means of a rope that makes an angle of 45.0° with the horizontal. If the mass of the sled is 60.0 kg and the coefficient of friction is 0.020, how much work is done in pulling the sled for a distance of 1.000 km?
Fap*cos45-u*mg = m*a
Fap*cos45-0.02*588 = m*0 = 0
Fap * cos45 - 11.76 = 0
Fap*cos45 = 11.76 N. = Hor. component of Force applied.
Work = 11.76 * 1000. = 11,760 Joules.
To calculate the work done in pulling the sled, we need to consider the frictional force acting on the sled and the gravitational force.
First, let's calculate the gravitational force:
1. The gravitational force is given by the formula: F_gravity = mass * acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s^2.
So, F_gravity = 60.0 kg * 9.8 m/s^2 = 588 N (Newton).
Next, let's calculate the frictional force:
1. The frictional force can be calculated using the formula: F_friction = coefficient of friction * normal force.
The normal force can be determined by considering the force components in the vertical direction.
Since the sled is on a horizontal surface, the normal force equals the gravitational force: F_normal = F_gravity = 588 N.
Therefore, F_friction = 0.020 * 588 N = 11.76 N.
Now, let's calculate the work done:
1. Work is equal to the force applied multiplied by the distance over which it acts.
The force applied is the horizontal component of the tension in the rope.
By considering the angle of 45.0°, the horizontal component of the tension is given by: F_horizontal = F_tension * cos(45.0°).
As the sled is being pulled horizontally, the force applied is equal to F_horizontal, which is also equal to the frictional force.
2. The distance over which the force acts is given as 1.000 km, but we need to convert it to meters.
1.000 km = 1000 m.
Now, we can calculate the work done:
1. Work = Force * Distance = F_friction * Distance = 11.76 N * 1000 m.
Work = 11760 J (Joules).
Therefore, the work done in pulling the sled for a distance of 1.000 km is 11760 Joules.