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FIGURE 9.1 shows a belt-drive system with a 230 mm driver pulley - NSC Mechanical Technology Welding and Metalwork - Question 9 - 2016 - Paper 1

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FIGURE 9.1 shows a belt-drive system with a 230 mm driver pulley. The belt speed in this system is 36 m·s⁻¹. The tensile force in the slack side is 140 N and the rat... show full transcript

Worked Solution & Example Answer:FIGURE 9.1 shows a belt-drive system with a 230 mm driver pulley - NSC Mechanical Technology Welding and Metalwork - Question 9 - 2016 - Paper 1

Step 1

Rotation frequency of the driver pulley in r/min

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Answer

To calculate the rotation frequency of the driver pulley, we can use the formula for belt speed:

V=πDnV = \pi D n

Where:

  • VV is the belt speed (36 m/s)
  • DD is the diameter of the driver pulley (0.23 m)
  • nn is the rotation frequency

Rearranging the formula to solve for nn:

n=VπDn = \frac{V}{\pi D}

Substituting the known values:

n=36π×0.2349.82 r/sn = \frac{36}{\pi \times 0.23} \approx 49.82 \text{ r/s}

To convert to r/min:

n49.82×602989.35 r/minn \approx 49.82 \times 60 \approx 2989.35 \text{ r/min}

Step 2

Power transmitted in this system

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Answer

The power transmitted can be calculated using the following formula:

P=(TtTs)×VP = (T_t - T_s) \times V

Where:

  • TtT_t is the tension in the tight side (350 N)
  • TsT_s is the tension in the slack side (140 N)
  • VV is the belt speed (36 m/s)
  • Tt=2.5×TsT_t = 2.5 \times T_s

First, calculate TtT_t:

Tt=2.5×140=350NT_t = 2.5 \times 140 = 350 N

Now substituting the values into the power equation:

P=(350140)×36=7560 WP = (350 - 140) \times 36 = 7560 \text{ W}

Therefore, the transmitted power is approximately 7.56 kW.

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