A block and a tackle system of 4 pulley is used to raise 150g vertically upward if the efficiency is 80% determine the minimum effort required to raise the load if g=10ms-2
To determine the minimum effort required to raise the load using a block and tackle system, we need to consider the concept of mechanical advantage and efficiency.
1. Mechanical Advantage (MA):
The mechanical advantage of a block and tackle system is calculated as the ratio of the load lifted (output force) to the effort applied (input force). In this case, the system consists of 4 pulleys, which results in a mechanical advantage of 4.
MA = Number of pulleys = 4
2. Efficiency (η):
Efficiency is defined as the ratio of the output work to the input work. In this case, the efficiency value is given as 80%, which can be converted to a decimal fraction:
η = 80% = 0.80
3. Calculating the load lifted:
The weight of the load is given as 150g. To convert this to kilograms, we divide by 1000:
Weight of the load = 150g / 1000 = 0.15 kg
4. Determining the minimum effort required:
The minimum effort required can be calculated by dividing the weight of the load by the product of mechanical advantage and efficiency:
Minimum effort = (Weight of the load) / (MA * Efficiency)
Minimum effort = 0.15 kg / (4 * 0.80)
Minimum effort = 0.15 kg / 3.20
Minimum effort = 0.0469 kg
5. Considering the acceleration due to gravity (g):
The value of g is given as 10 m/s^2.
Finally, to calculate the minimum effort required in Newtons (N), we multiply the mass by the acceleration due to gravity:
Minimum effort = 0.0469 kg * 10 m/s^2
Minimum effort = 0.469 N
Therefore, the minimum effort required to raise the load is approximately 0.469 Newtons.
To determine the minimum effort required to raise the load using a block and tackle system of 4 pulleys, we need to understand the concept of efficiency and how it relates to the mechanical advantage of the system.
Efficiency is defined as the ratio of output power to input power, expressed as a percentage. In this case, the input power refers to the effort force (F_effort) applied to the system, and the output power is the weight being lifted (W_load) multiplied by the gravity acceleration (g = 10 m/s^2) and the distance it is lifted (d).
The formula for efficiency is:
Efficiency = (Output power / Input power) * 100
Given that efficiency is 80%, we can rewrite the formula as:
0.8 = (W_load * g * d) / (F_effort * d)
The distance (d) cancels out, so the equation becomes:
0.8 = (W_load * g) / F_effort
Now, we can rearrange the equation to solve for the minimum effort force (F_effort):
F_effort = (W_load * g) / 0.8
Plugging in the values we know:
W_load = 150 g (given weight)
g = 10 m/s^2 (acceleration due to gravity)
Efficiency = 0.8 (80% as a decimal)
F_effort = (150 g * 10 m/s^2) / 0.8
Simplifying, we have:
F_effort = 1875 g N
where N represents the unit of force, the Newton (N).
Therefore, the minimum effort required to raise the load using a block and tackle system of 4 pulleys is 1875 g Newtons.