A rope is tied to a box and used to pull the box 1.7 m along a horizontal floor. The rope makes an angle of 30∘ with the horizontal and has a tension of 5 N. The opposing friction force between the box and the floor is 1 N.
Part A
How much work does gravity do on the box?
Part B
How much work does the tension in the rope do on the box?
Part C
How much work does the friction do on the box?
Part D
How much work does the normal force do on the box?
Part E
What is the total work done on the box?
A) Gravity is NOT in the direction of motion, so ZERO
B) 5 cos 30 * 1.7
C) -1 * 1.7
D) Same answer as A
E) B-C
Part A: Gravity doesn't do any work on the box because it acts perpendicular to the displacement.
Part B: The tension in the rope does positive work on the box. The work can be calculated using the formula: work = force * displacement * cos(angle). In this case, force = 5 N, displacement = 1.7 m, and the angle is 30 degrees. Plugging in the values, we get work = 5 N * 1.7 m * cos(30°).
Part C: Friction does negative work on the box because it acts opposite to the direction of motion. The work can be calculated using the formula: work = force * displacement * cos(angle). In this case, force = 1 N, displacement = 1.7 m, and the angle is 180 degrees (opposite direction of motion). Plugging in the values, we get work = 1 N * 1.7 m * cos(180°).
Part D: The normal force doesn't do any work on the box because it acts perpendicular to the displacement.
Part E: The total work done on the box is the sum of the work done by tension and friction. To calculate the total work, add the work from part B (tension) and the work from part C (friction).
To solve this problem, we need to use the work-energy principle. The work done on an object is equal to the force applied to the object multiplied by the distance the object moves in the direction of the force.
Part A: How much work does gravity do on the box?
The weight of the box is given by the formula: Weight = mass × acceleration due to gravity.
To find the work done by gravity, we need to calculate the vertical distance that the box moves against the force of gravity.
Given:
Force of gravity = Weight = mass × acceleration due to gravity = m × g
Mass of the box = m
Acceleration due to gravity = g = 9.8 m/s²
Vertical distance moved by the box = 0 since it moves horizontally.
Work done by gravity = Force of gravity × vertical distance moved = m × g × 0 = 0
Therefore, the work done by gravity on the box is 0.
Part B: How much work does the tension in the rope do on the box?
To find the work done by tension, we need to calculate the horizontal distance that the box moves in the direction of the tension force.
Given:
Force of tension = 5 N
Horizontal distance moved by the box = 1.7 m
Work done by tension = Force of tension × horizontal distance moved = 5 N × 1.7 m = 8.5 J
Therefore, the work done by the tension in the rope on the box is 8.5 J.
Part C: How much work does the friction do on the box?
To find the work done by friction, we need to calculate the distance that the box moves against the friction force. Since the box moves horizontally, the distance moved is the same as the distance moved by the tension force.
Given:
Friction force = 1 N
Horizontal distance moved by the box = 1.7 m
Work done by friction = Friction force × horizontal distance moved = 1 N × 1.7 m = 1.7 J
Therefore, the work done by the friction force on the box is 1.7 J.
Part D: How much work does the normal force do on the box?
The normal force acts perpendicular to the direction of motion, so it does no work. Therefore, the work done by the normal force on the box is 0 J.
Part E: What is the total work done on the box?
To find the total work done on the box, we need to sum up the work done by all the forces involved.
Total work done = Work done by tension + Work done by friction + Work done by gravity + Work done by normal force
Total work done = 8.5 J + 1.7 J + 0 J + 0 J
Total work done = 10.2 J
Therefore, the total work done on the box is 10.2 J.
To find the work done in each scenario, we can use the formula:
Work = Force x Distance x Cos(θ)
where:
- Work is the amount of work done
- Force is the force acting on the object
- Distance is the distance through which the object is displaced
- θ is the angle between the force and the direction of displacement (in degrees)
Let's calculate the work done in each situation:
Part A: How much work does gravity do on the box?
In this case, the force of gravity is acting vertically downward, and the box is displaced horizontally. Hence, the angle between the force of gravity and the displacement is 90 degrees.
Work_gravity = Force_gravity x Distance x Cos(90)
The force of gravity can be calculated using the formula:
Force_gravity = mass x acceleration due to gravity
Assuming the mass of the box is given, we can find the force of gravity. Then, we substitute the values into the equation.
Part B: How much work does the tension in the rope do on the box?
Here, the tension in the rope is acting at an angle of 30 degrees with the horizontal, which is also the direction of displacement.
Work_tension = Force_tension x Distance x Cos(30)
The tension in the rope has already been given.
Part C: How much work does friction do on the box?
The friction force is opposing the motion of the box. The angle between the friction force and the displacement is 180 degrees, as they are in exactly opposite directions.
Work_friction = Force_friction x Distance x Cos(180)
The opposing friction force has already been given.
Part D: How much work does the normal force do on the box?
The normal force is acting perpendicular to the surface of the floor, which is perpendicular to the direction of displacement. Therefore, the angle between the normal force and the displacement is 90 degrees.
Work_normal = Force_normal x Distance x Cos(90)
The normal force can be calculated using the formula:
Force_normal = mass x acceleration due to gravity
Assuming the mass of the box is given, we can find the force of gravity. Then, we substitute the values into the equation.
Part E: What is the total work done on the box?
The total work done on the box is the sum of the work done by each force (gravity, tension, friction, and normal force).
Total_work = Work_gravity + Work_tension + Work_friction + Work_normal
By calculating each part individually, we can find the total work done on the box.