Question

If a person and wheelchair have a combined weight of 185 lb, how much ideal effort

Answer 1

Answer:

Effort force$=824.04 \sin\theta$

where $\theta$ is the angle of inclination of the ramp.

Explanation:

The given combined mass of a person and wheelchair is 185 lb.

In SI unit, 1 pound= 0.453592 kg

So, 185 lb=$185\times0.453592$ kg=84kg (approximately)

Assuming the whole mass as a point mass and denote it by M, so

M=84kg

Let the angle of inclination of the ram with the is $\theta$ with respect to the ground and assume that the friction offered by ram id negligible, so neglection the frictional force.

The applied effort force, F, will be minimum when applied in the direction parallel to the ramp surface as shown in the figure.

The gravitational force action on M is Mg in the downward direction.

For the mass M to be at an equilibrium condition on the ramp, the sum of the total force in any direction will be zero.

Equate the sum of all the forces in the direction parallel to the ramp to zero.

$F-Mg\sin\theta=0$

$\Rightarrow F=Mg \sin\theta$

$\Rightarrow F=84\times 9.81\sin\theta$

$\Rightarrow F=824.04\sin\theta N$.