Physics High School

A 0.050 kg yo-yo is swung in a vertical circle on the end of its 0.30 m long string at the slowest speed that the yo-yo can have. (8 marks)

a) What is this speed at the top of the circular path? Include a labelled free-body diagram with your answer.

b) What is this speed at the bottom of the circular path?

c) What will the maximum tension in the string be when the yo-yo is swung in the vertical circle at the slowest speed? Where will this maximum tension occur? Include a labelled free-body diagram with your answer.

Answers

Answer 1

a) The speed of the yo-yo at the top of the circular path is given by:

v² = gr [r + h]

Where, v = velocity

g = acceleration due to gravity

r = radius

h = height

Here, r = 0.30m (length of the string)

h = r

  = 0.30m (height of the circle at the top)

g = 9.8 m/s²

Putting these values in the above equation,

v = √(9.8 × 0.6) = 3.4 m/s

The free-body diagram for the yo-yo at the top of the circular path is given below:

b) The speed of the yo-yo at the bottom of the circular path is given by:

v² = gr [r - h]

Where, v = velocity

g = acceleration due to gravity

r = radius

h = height

Here, r = 0.30m (length of the string)

h = r

  = 0.30m (height of the circle at the bottom)

g = 9.8 m/s²

Putting these values in the above equation,

v = √(9.8 × 0.0)

  = 0 m/s

The free-body diagram for the yo-yo at the bottom of the circular path is given below:

c) The maximum tension in the string occurs when the yo-yo is at the bottom of the circular path. At this point, the tension in the string provides the centripetal force required to keep the yo-yo moving in a circular path. The maximum tension in the string is given by:

T = mg + mv² / r

Where, T = tension in the string

m = mass of the yo-yo

v = velocity

r = radius

g = acceleration due to gravity

At the slowest speed, v = 0 and hence, the maximum tension in the string is given by:

T = mg + 0

  = mg

  = 0.050 × 9.8

  = 0.49 N

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Related Questions


A machine is used to form bubbles from pure water by
mechanically foaming it. The surface tension of water is 0:070 N
m-1. What is the gauge pressure inside bubbles of radius 10 m?

Answers

The gauge pressure inside the bubble is 14,000 N/m² or 14,000 Pa. We can use Laplace's law for pressure inside a curved liquid interface: ΔP = 2σ/R.

To find the gauge pressure inside bubbles, we can use the Laplace's law for pressure inside a curved liquid interface:

ΔP = 2σ/R

where ΔP is the pressure difference across the curved interface, σ is the surface tension of water, and R is the radius of the bubble.

Given:

Surface tension of water (σ) = 0.070 N/m

Radius of the bubble (R) = 10 μm = 10 × 10^(-6) m

Substituting the values into the equation, we have:

ΔP = 2σ/R

= 2 * 0.070 / (10 × 10^(-6))

= 14,000 N/m²

The gauge pressure is the difference between the absolute pressure inside the bubble and the atmospheric pressure. Since the problem only asks for the gauge pressure, we assume the atmospheric pressure to be zero.

Therefore, the gauge pressure inside the bubble is 14,000 N/m² or 14,000 Pa.

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