Find the work done when a 20 kg sled is pulled across level ground by a rope that makes a 50 deg angle with the horizontal. The sled moves 40 m and the rope is pulled with 10 N of force. If the work done by friction is 240 J, what will happen to the Kinetic Energy of the sled?
Work done by rope:
W = 10*cos50*40 = 257.1 J
If friction uses up 240 J of this work, there are still 17.1 J left to increase the kinetic energy of the sled.
To find the work done, we can use the formula:
Work = Force × displacement × cos(angle)
Given information:
Mass of the sled (m) = 20 kg
Displacement (d) = 40 m
Force applied (F) = 10 N
Angle with the horizontal (θ) = 50 degrees
First, let's find the work done by the force pulling the sled:
Work = 10 N × 40 m × cos(50°)
Work = 10 N × 40 m × cos(50°)
Work = 400 Nm × cos(50°) (Since 1 Nm = 1 J)
Work = 400 J × 0.643 (cos(50°) ≈ 0.643)
Work ≈ 257.2 J
Next, let's find the work done against friction:
Work done by friction = -240 J (negative because the friction is working against the motion)
Now, we can find the net work done:
Net Work = Work done by force - Work done by friction
Net Work = 257.2 J - (-240 J)
Net Work = 257.2 J + 240 J
Net Work = 497.2 J
The work done on an object is equal to the change in kinetic energy. So, if the net work done is positive (as it is in this case), the kinetic energy of the sled will increase.
To find the work done when pulling the sled, we need to calculate the dot product between the force and the displacement vectors. The formula for work is:
Work = Force * Distance * cos(theta)
where:
- Force is the applied force in the direction of motion,
- Distance is the displacement,
- theta is the angle between the force and the displacement vectors.
In this case, the applied force is 10 N, the displacement is 40 m, and the angle theta is 50 degrees.
First, let's convert the angle to radians:
theta_radians = 50 degrees * (pi / 180) ≈ 0.8727 rad
Now, we can calculate the work done:
Work = 10 N * 40 m * cos(0.8727 rad)
Using a calculator, we find:
Work ≈ 328.57 J
The work done by friction is given as 240 J.
Now, to determine what will happen to the Kinetic Energy of the sled, we need to compare the work done to the work done by friction.
If the work done by friction is greater than the work done by pulling the sled, then the frictional force has done more work against the motion, resulting in a decrease in the sled's Kinetic Energy.
If the work done by friction is less than the work done by pulling the sled, then the pull force has done more work, causing an increase in the sled's Kinetic Energy.
In this case, the work done by pulling the sled (328.57 J) is greater than the work done by friction (240 J). Therefore, the pull force has done more work, causing an increase in the sled's Kinetic Energy.