Aperson stands a distance r from a door's hinges and pushes with a force f directed perpendicular to its surface. by what factor does the applied torque change if the person's position and force change to the following? use the definition of torque, with θ = 90°.(a) 2r and 2f(b) 2r and f(c) r and f/2(d) r/2 and f/2

a)

4 times

b)

2 times

c)

0.5 times

d)

0.25 times

Explanation:

= Applied force by the person = F

= distance from the hinge = R

Torque is given as

(a)

= Applied force by the person = 2F

= distance from the hinge = 2R

New Torque is given as

So Torque becomes 4 times

b)

= Applied force by the person = F

= distance from the hinge = 2R

New Torque is given as

So Torque becomes 2 times

c)

= Applied force by the person = (0.5)F

= distance from the hinge = R

New Torque is given as

So Torque becomes 0.5 times

d)

= Applied force by the person = (0.5)F

= distance from the hinge = (0.5)R

New Torque is given as

So Torque becomes 0.25 times

as a general rule, scissors have blades less than 6 in (15 cm) long and usually have handles with finger holes of the same size. shears have blades scissors used to cut hair or fabric must be much sharper