Home > Physics > Simple Machines

An object with a mass of #3 kg# is hanging from an axle with a radius of #6 cm#. If the wheel attached to the axle has a radius of #12 cm#, how much work would it take to turn the wheel #3 cm#?

Answer 1

Nathan Ashcroft

The work done is #=0.44J#

The load #=(3g)N#

Radius of axle #r=0.06m#

Radius of wheel #R=0.12m#

Taking moments about the center of the axle

#F*0.12=3*g*0.06#

#F=(3*g*0.06)/0.12=3/2g=14.7N#

The work done is

#W=F*d=14.7*0.03=0.44J#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nora Arzate

Use the work formula for rotating objects:

[ W = \tau \cdot \theta ]

where ( \tau = r \cdot F ) (torque), ( F = m \cdot g ) (force due to gravity), ( r = 0.06 \ \text{m} ) (radius of the axle), ( \theta = \frac{d}{r_w} ) (angular displacement), ( r_w = 0.12 \ \text{m} ) (radius of the wheel).

[ F = 3 \ \text{kg} \cdot 9.8 \ \text{m/s}^2 ] [ \tau = 0.06 \ \text{m} \cdot (3 \ \text{kg} \cdot 9.8 \ \text{m/s}^2) ] [ \theta = \frac{0.03 \ \text{m}}{0.12 \ \text{m}} ]

[ W = (0.06 \ \text{m} \cdot 3 \ \text{kg} \cdot 9.8 \ \text{m/s}^2) \cdot \frac{0.03 \ \text{m}}{0.12 \ \text{m}} ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.