An object with a mass of #4 kg# is hanging from an axle with a radius of #8 cm#. If the wheel attached to the axle has a radius of #24 cm#, how much work would it take to turn the wheel #4 cm#?

Question

An object with a mass of #4  kg# is hanging from an axle with a radius of #8 cm#.  If the wheel attached to the axle has a radius of #24 cm#, how much work would it take to turn the wheel #4 cm#?

Emily Abbate · Accepted Answer

The work is #=0.52J#

The load is #L=4gN#

The radius of the axle is #r=0.08m#

The radius of the wheel is #R=0.24m#

The effort is #=FN#

Taking moments about the center of the axle

#F*0.24=4g*0.08#

Plugging in the value of #g=9.8ms^-2#

#F=4g*0.08/0.24=13.07N#

The force is #F=13.07N#

The distance is #=0.04m#

The work is #W=Fd=13.07*0.04=0.52J#

Nicholas Agrusa · Answer

undefined To calculate the work required to turn the wheel by 4 cm, we first need to find the distance the object moves when the wheel turns by 4 cm. Since the axle and the object are connected, they move together. The ratio of the radii of the axle and the wheel is 1:3 (8 cm : 24 cm), so the distance the object moves is 4 cm * 3 = 12 cm.

Next, we calculate the work done using the formula:

$$Work = Force \times Distance$$

The force required to move the object is equal to the force of gravity acting on it, which is $mass \times gravitational\ acceleration = 4 kg \times 9.81 m/s^2$.

Plugging in the values, we get:

$$Work = 4 kg \times 9.81 m/s^2 \times 0.12 m$$

$$Work = 4.7052 N \times 0.12 m$$

$$Work = 0.5646 Nm$$

Therefore, it would take approximately 0.5646 Nm of work to turn the wheel by 4 cm.