A student pulls a (34) kg box a distance of (13.50) m up a ramp set at 25.8o using a force of (181) N applied parallel to the ramp. Find the efficiency of the ramp. Give your answer in percent (%) and with 3 significant figures.
work done=34*9.8*13.5*sin25.8
work applied=181*13.5
efficiency=workdone/workapplied *100
To find the efficiency of the ramp, we need to determine the work input and the work output.
The work input represents the work done by the student in pulling the box up the ramp, while the work output represents the useful work done by the ramp on the box.
The work input (W_input) can be calculated using the equation:
W_input = force * distance * cos(angle)
W_input = (181 N) * (13.50 m) * cos(25.8°)
Let's calculate the work input:
W_input = 181 N * 13.50 m * cos(25.8°)
Next, we need to calculate the work output (W_output) done by the ramp on the box. The work output is equal to the weight of the box multiplied by the vertical height it is lifted.
The weight of the box can be calculated using the formula:
Weight = mass * gravity
Weight = 34 kg * 9.8 m/s^2
Let's calculate the weight of the box:
Weight = 34 kg * 9.8 m/s^2
Now, we can calculate the work output (W_output):
W_output = weight * distance_lifted
W_output = (weight of box) * (vertical height)
Next, we need to convert the work input and work output into percentages to find the efficiency.
The efficiency (E) is given by the formula:
E = (W_output / W_input) * 100
Let's substitute the values and calculate the efficiency:
E = (W_output / W_input) * 100
Finally, we round the efficiency to 3 significant figures.
I will calculate the actual values and provide the final answer.
To find the efficiency of the ramp, we need to first determine the work done by the student in pulling the box up the ramp, and then calculate the work done against gravity.
1. Calculate the work done by the student:
The work done by the student can be calculated using the formula: Work = Force x Distance x cos(θ), where θ is the angle between the force and the displacement. In this case, the force applied by the student is 181 N, and the distance is 13.50 m. The angle θ is given as 25.8°.
Work = 181 N x 13.50 m x cos(25.8°)
Work = 3362.35 N·m
2. Calculate the work done against gravity:
The work done against gravity can be calculated using the formula: Work = Force x Distance, where the force is the weight of the box and the distance is the height the box is lifted. In this case, the weight of the box can be calculated using the equation: weight = mass x gravity, where the mass is 34 kg, and the acceleration due to gravity is approximately 9.81 m/s^2. The distance is the vertical height the box is lifted, which can be calculated using the formula: height = distance x sin(θ).
Weight of the box = mass x gravity
Weight of the box = 34 kg x 9.81 m/s^2
Weight of the box = 332.54 N
Height = distance x sin(θ)
Height = 13.50 m x sin(25.8°)
Height = 5.62 m
Work = Force x Distance
Work = 332.54 N x 5.62 m
Work = 1868.08 N·m
3. Calculate the efficiency:
The efficiency of the ramp is calculated by dividing the work done against gravity by the work done by the student, and then multiplying by 100 to express it as a percentage.
Efficiency = (Work done against gravity / Work done by the student) x 100
Efficiency = (1868.08 N·m / 3362.35 N·m) x 100
Efficiency ≈ 55.512%
Therefore, the efficiency of the ramp is approximately 55.5% when rounded to three significant figures.