A rope that is at 35° to the horizontal is used to pull 10kg crate across a rough floor.
The crate is initially at rest and is dragged for a distance of 4.0m. The tension in the rope is 60N and the frictional force opposing the motion is 10N.
A) Calculate the work done on the crate by the tension in the rope.
B) Find the net work done on the crate.
C) Determine the energy lost from the system as heat and sound due to the frictional force.
A) 60 N cos 35 * 4.0 m = 196.6 J
B) 60 N cos 35 * 4.0 m - 10 N*4.0 m = ?
C) 10N*4.0m = 40 J
or (A) - (B), in terms of previous answers.
To solve this problem, we'll need to use some basic principles of physics and work-energy theorem. Let's break it down step by step:
A) Calculate the work done on the crate by the tension in the rope.
Work (W) is defined as the force applied in the direction of motion multiplied by the displacement. In this case, the force applied is the tension in the rope (60N) and the displacement is the distance the crate is dragged (4.0m).
The formula for work is given by: W = force * displacement * cos(angle)
In this case, the angle is 35° to the horizontal. So we have:
W = 60N * 4.0m * cos(35°)
W = 240 N*m * cos(35°)
W = 240 N*m * 0.819
W ≈ 196.56 Joules (J)
Therefore, the work done on the crate by the tension in the rope is approximately 196.56 Joules.
B) Find the net work done on the crate.
The net work done on an object is the total work done on it, taking into account all the forces acting on it. In this case, we have two forces acting on the crate: the tension in the rope and the frictional force opposing the motion.
The formula for net work is given by: Net work = work by tension - work by friction
We have already found the work by tension in part A, which is 196.56 J.
The work by friction can be calculated using the formula: work by friction = frictional force * displacement * cos(180°), as frictional force acts in the opposite direction of motion.
So we have:
Work by friction = 10N * 4.0m * cos(180°)
Work by friction = -40 N*m * cos(180°)
Work by friction = -40 N*m * (-1)
Work by friction = 40 Joules (J)
Now, we can calculate the net work done:
Net work = 196.56 J - 40 J
Net work ≈ 156.56 Joules
Therefore, the net work done on the crate is approximately 156.56 Joules.
C) Determine the energy lost from the system as heat and sound due to the frictional force.
The work done by the frictional force represents the energy lost from the system as heat and sound. In this case, the work done by friction is 40 Joules.
Therefore, the energy lost from the system as heat and sound due to the frictional force is 40 Joules.