18. A wheel and axle have radii 80cm and 10 cm respectively. If the efficiency of the machine is 0.85, what load will an applied force of 1200N to the wheel raise?

Question

18. A wheel and axle have radii 80cm and 10 cm respectively. If the efficiency of the machine is 0.85, what load will an applied force of 1200N to the wheel raise?

Asked on March 29, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-03-29T15:22:33.289Z

18. A wheel and axle have radii 80cm and 10 cm respectively. If the efficiency of the machine is 0.85, what load will an applied force of 1200N to the wheel raise? Given: Wheel radius $R_W = 80 \text{ cm} = 0.8 \text{ m}$ Axle radius $R_A = 10 \text{ cm} = 0.1 \text{ m}$ Efficiency $\eta = 0.85$ Applied force (Effort) $F_E = 1200 \text{ N}$ Step 1: Calculate the Velocity Ratio (VR). The velocity ratio for a wheel and axle is the ratio of the wheel's radius to the axle's radius. $$ VR = \frac{R_W}{R_A} $$ $$ VR = \frac{0.8 \text{ m}}{0.1 \text{ m}} = 8 $$ Step 2: Calculate the Mechanical Advantage (MA). The efficiency of a machine is given by the ratio of its mechanical advantage to its velocity ratio. $$ \eta = \frac{MA}{VR} $$ Rearrange to solve for MA: $$ MA = \eta \times VR $$ $$ MA = 0.85 \times 8 $$ $$ MA = 6.8 $$ Step 3: Calculate the Load ($F_L$). The mechanical advantage is also defined as the ratio of the load to the effort. $$ MA = \frac{F_L}{F_E} $$ Rearrange to solve for $F_L$: $$ F_L = MA \times F_E $$ $$ F_L = 6.8 \times 1200 \text{ N} $$ $$ F_L = 8160 \text{ N} $$ The load that an applied force of $1200 \text{ N}$ will raise is $\boxed{8160 \text{ N}}$.

Accepted Answer · 2026-03-29T15:22:33.289Z

18. A wheel and axle have radii 80cm and 10 cm respectively. If the efficiency of the machine is 0.85, what load will an applied force of 1200N to the wheel raise? Given: Wheel radius $R_W = 80 \text{ cm} = 0.8 \text{ m}$ Axle radius $R_A = 10 \text{ cm} = 0.1 \text{ m}$ Efficiency $\eta = 0.85$ Applied force (Effort) $F_E = 1200 \text{ N}$ Step 1: Calculate the Velocity Ratio (VR). The velocity ratio for a wheel and axle is the ratio of the wheel's radius to the axle's radius. $$ VR = \frac{R_W}{R_A} $$ $$ VR = \frac{0.8 \text{ m}}{0.1 \text{ m}} = 8 $$ Step 2: Calculate the Mechanical Advantage (MA). The efficiency of a machine is given by the ratio of its mechanical advantage to its velocity ratio. $$ \eta = \frac{MA}{VR} $$ Rearrange to solve for MA: $$ MA = \eta \times VR $$ $$ MA = 0.85 \times 8 $$ $$ MA = 6.8 $$ Step 3: Calculate the Load ($F_L$). The mechanical advantage is also defined as the ratio of the load to the effort. $$ MA = \frac{F_L}{F_E} $$ Rearrange to solve for $F_L$: $$ F_L = MA \times F_E $$ $$ F_L = 6.8 \times 1200 \text{ N} $$ $$ F_L = 8160 \text{ N} $$ The load that an applied force of $1200 \text{ N}$ will raise is $\boxed{8160 \text{ N}}$.