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Calculate the velocity ratio, weight of cement bag, mechanical advantage, and efficiency of the pulley system shown in Figure 4, given the effort is 300 N and the cement bag's mass is 50 kg.

Physics

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Step-by-step solution

7 steps

Part a· 1 step

What is the velocity ratio of the machine?

  1. Determine the number of rope segments supporting the movable load.

    In Figure 4, there are 3 rope segments supporting the lower block (which carries the load).

    The velocity ratio (VR) is the number of rope segments supporting the movable load.

    VR=3VR = 3

    The velocity ratio of the machine is 3\boxed{\text{3}}.

Part b· 2 steps

Calculate the weight of the bag of cement.

  1. Identify the mass of the cement bag and the acceleration due to gravity.

    Mass (mm) = 50 kg
    Acceleration due to gravity (gg) ≈10 m/s2\approx 10 \text{ m/s}^2 (standard approximation for such problems unless specified otherwise).

  2. Calculate the weight using the formula W=m×gW = m \times g.

    W=50 kg×10 m/s2W = 50 \text{ kg} \times 10 \text{ m/s}^2 W=500 NW = 500 \text{ N}

    The weight of the bag of cement is 500 N\boxed{\text{500 N}}.

Part c· 2 steps

Calculate the mechanical advantage of the pulley system.

  1. Identify the load and the effort.

    Load (LL) = Weight of the bag of cement = 500 N (from part b)
    Effort (EE) = 300 N (given in the problem description)

  2. Calculate the mechanical advantage (MA) using the formula MA=LEMA = \frac{L}{E}.

    MA=500 N300 NMA = \frac{500 \text{ N}}{300 \text{ N}} MA=53MA = \frac{5}{3} MA≈1.67MA \approx 1.67

    The mechanical advantage of the pulley system is 1.67\boxed{\text{1.67}}.

Part d· 2 steps

Calculate the efficiency of the pulley system.

  1. Identify the mechanical advantage (MA) and velocity ratio (VR).

    MA = 1.67 (from part c)
    VR = 3 (from part a)

  2. Calculate the efficiency (η\eta) using the formula η=MAVR×100%\eta = \frac{MA}{VR} \times 100\%.

    η=1.673×100%\eta = \frac{1.67}{3} \times 100\% η≈0.5567×100%\eta \approx 0.5567 \times 100\% η≈55.67%\eta \approx 55.67\%

    The efficiency of the pulley system is 55.67%\boxed{\text{55.67\%}}.

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