An 7.5 crate is pulled 5.4 up a 30 degree incline by a rope angled 19 degrees above the incline. The tension in the rope is 130N and the crate's coefficient of kinetic friction on the incline is 0.24.
How much work is done by tension? by gravity? by the normal force?
To determine how much work is done by tension, gravity, and the normal force, we need to understand the concepts of work and the forces involved in the given scenario.
Work is defined as the transfer of energy that occurs when a force is applied to an object, causing it to move in the direction of the force. Mathematically, work is given by the equation:
Work = Force * Distance * cos(theta)
In this equation, Force represents the applied force, Distance represents the distance over which the force is applied, and theta represents the angle between the force and the direction of motion.
Now let's break down the forces involved:
1. Tension Force: The tension force is applied by the rope. It acts in the upward direction and helps to pull the crate up the incline. To calculate the work done by tension, we need to determine the distance the crate moves in the direction of the force. In this case, the distance is given as 5.4 meters. Since the force and direction of motion are aligned, the angle between them is 0 degrees.
Work done by tension = Tension Force * Distance * cos(0)
Work done by tension = 130N * 5.4m * cos(0)
Work done by tension = 702 J (joules)
2. Gravity Force: The force of gravity acts vertically downward due to the weight of the crate. To calculate the work done by gravity, we need to determine the vertical distance the crate moves. Since the crate is being pulled up the incline, it does not move vertically. Therefore, the work done by gravity is zero.
Work done by gravity = 0 J (joules)
3. Normal Force: The normal force acts perpendicular to the incline and prevents the crate from sinking into the incline. Since the crate does not move in the direction of the normal force, the work done by the normal force is also zero.
Work done by the normal force = 0 J (joules)
In summary:
Work done by tension = 702 J (joules)
Work done by gravity = 0 J (joules)
Work done by the normal force = 0 J (joules)
<<How much work is done by tension?>>
(tension component up incline)*(distance)
<< by gravity?>>
-(vertical rise)*(weight)
<<by the normal force?>>
zero, because it is perpendicular to the motion
Your 7.5 and 5.4 numbers require dimensions. Surely you have learned that by now.