Chapter 10

If the IMA of a ramp is \(4.0\) and its AMA is \(3.2\), what is its efficiency?

Given \(F_{R} \cdot s_{R}=F_{E} \cdot s_{E}\), find each missing quantity. $$ F_{R} $$ \(F_{E}\) \(s_{R}\) \(s_{E}\) \(\begin{array}{llll}20.0 \mathrm{~N} & 5.00 \mathrm{~N} & 3.70 \mathrm{~cm} & \mathrm{~cm}\end{array}\)

If the AMA of a wheel-and-axle is \(9.0\) and its IMA is 13 , what is its efficiency?

Given \(F_{R} \cdot s_{R}=F_{E} \cdot s_{E}\), find each missing quantity. $$ F_{R} $$ \(F_{E}\) \(s_{R}\) \(s_{E}\) \(\mathrm{N}\) \(176 \mathrm{~N}\) \(49.2 \mathrm{~cm}\) \(76.3 \mathrm{~cm}\)

If the efficiency of a screw is \(32 \%\) and its IMA is \(4 \overline{0}\), what is its AMA?

Given \(F_{R} \cdot s_{R}=F_{E} \cdot s_{E}\), find each missing quantity. $$ F_{R} $$ \(F_{E}\) \(s_{R}\) \(s_{E}\) \(37.0 \mathrm{~N}\) \(12.0 \mathrm{~N}\) 0 0 \(\mathrm{cm}\) 0 \(112 \mathrm{~cm}\)

If the efficiency of lever is \(94 \%\) and its AMA is 12 , what is its IMA?

Given \(F_{R} \cdot s_{R}=F_{E} \cdot s_{E}\), find each missing quantity. $$ F_{R} $$ \(F_{E}\) \(s_{R}\) \(s_{E}\) \(9.80\) in. \(\quad 53.9 \mathrm{in}\). \(23.4 \mathrm{lb} \quad 9.80 \mathrm{lb}\)

If the IMA of an inclined plane is \(6.0\) and its AMA is \(4.8\), what is its efficiency?

Given \(F_{R} \cdot s_{R}=F_{E} \cdot s_{E}\), find each missing quantity. $$ F_{R} $$ \(F_{E}\) \(s_{R}\) \(s_{E}\) \(119 \mathrm{~N}\) \(\mathrm{N}\) \(29.7 \mathrm{~cm}\) \(67.4 \mathrm{~cm}\)

If the AMA of a ramp is \(4.6\) and its IMA is \(6.0\), what is its efficiency?

If the IMA of a pulley is 12 and its AMA is \(9.0\), what is its efficiency?

If the IMA of a screw is \(6 \overline{0}\) and its AMA is 26 , what is its efficiency?

Given \(\mathrm{MA}_{\text {screw }}=\frac{2 \pi r}{\text { pitch }}\), find each missing quantity. $$ 7.40 \mathrm{~mm} \quad 1.32 \mathrm{~mm} $$

If the efficiency of a pulley is \(82 \%\) and its IMA is 22 , what is its AMA?

A wheel-and-axle has an efficiency of \(65 \%\). If its AMA is 16 , what is its IMA?

An inclined plane is \(10.0 \mathrm{~m}\) long and \(2.50 \mathrm{~m}\) high. (a) Find its mechanical advantage. (b) A resistance of \(727 \mathrm{~N}\) is pushed up the plane. What effort is needed? (c) An effort of \(20 \overline{0} \mathrm{~N}\) is applied to push an \(815-\mathrm{N}\) resistance up the inclined plane. Is the effort enough?

A wheel with radius \(75.0 \mathrm{~cm}\) is attached to an axle of radius \(13.6 \mathrm{~cm} .\) What force must be applied to the rim of the wheel to raise a \(1000-\mathrm{N}\) weight?

An axle of radius \(12.0 \mathrm{~cm}\) is used with a wheel of radius \(62.0 \mathrm{~cm}\). What force must be applied to the rim of the wheel to lift a weight of \(975 \mathrm{~N}\) ?

A wood screw with pitch \(0.125\) in. is advanced into wood using a screwdriver whose handle is \(1.50\) in. in diameter. (a) What is the mechanical advantage of the screw? (b) What is the resistance of the wood if \(15.0 \mathrm{lb}\) of effort is applied on the wood screw? (c) What is the resistance of the wood if \(15.0 \mathrm{lb}\) of effort is applied to the wood screw using a screwdriver whose handle is \(0.500\) in. in diameter?

A 3.00-m-long plank is used to raise a cooling unit \(1.00 \mathrm{~m}\). What is the MA of the ramp made by the plank?

The radius of the axle of a winch is \(3.00\) in. The length of the handle (radius of wheel) is \(1.50 \mathrm{ft}\). (a) What weight will be lifted by an effort of \(73.0 \mathrm{lb}\) ? (b) Find the MA.

The handle of a jackscrew is \(60.0 \mathrm{~cm}\) long. (a) If the mechanical advantage is \(78.0\), what is the pitch? (b) How much weight can be raised by applying a force of \(43 \overline{0} \mathrm{~N}\) to the jackscrew handle?

A \(2.75\) -m-long board is used to slide a compressor a vertical distance of \(0.750 \mathrm{~m}\). What is the MA of the ramp made by the board?

A resistance of \(325 \mathrm{~N}\) is raised by using a ramp \(5.76 \mathrm{~m}\) long and by applying a force of \(75.0 \mathrm{~N}\). (a) How high can it be raised? (b) Find the MA of the ramp.

The diameter of the wheel of a wheel-and-axle is \(10.0 \mathrm{~cm} .\) (a) If a force of \(475 \mathrm{~N}\) is raised by applying a force of \(142 \mathrm{~N}\), find the diameter of the axle. (b) Find the MA.

A pole is used to lift a car that fell off a jack (Fig. \(10.9)\). The pivot is \(2.00 \mathrm{ft}\) from the car. Two people together exert \(275 \mathrm{lb}\) of force \(8.00 \mathrm{ft}\) from the pivot. (a) What force is applied to the car? (Disregard the weight of the pole.) (b) Find the MA.

A plank \(12 \mathrm{ft}\) long is used as an inclined plane to a platform \(3.0\) ft high. (a) What force must be used to push a load weighing 480 lb up the plank? (b) Find the MA of the inclined plane.

Two persons use a large winch to raise a mass of \(470 \mathrm{~kg}\). The radius of the wheel is \(48 \mathrm{~cm}\) and the radius of the axle is \(4.0 \mathrm{~cm}\). (a) What force is required to lift the load? (b) Find the MA of the large winch. (c) If the efficiency of the large winch is \(60 \%\) and each person exerts the same force, how much force must each apply?

A bar is used to lift a \(10 \overline{0}\) -kg block of concrete. The pivot is \(1.00 \mathrm{~m}\) from the block. (a) If the worker pushes down on the other end of the bar a distance of \(2.50 \mathrm{~m}\) from the pivot, what force (in \(\mathrm{N}\) ) must the worker apply? (b) Find the MA.

A system consisting of two fixed pulleys and two movable pulleys has a mechanical advantage of 4 . (a) If a force of \(97.0 \mathrm{~N}\) is exerted, what weight is raised? (b) If the weight is raised \(20.5 \mathrm{~m}\), what length of rope is pulled?

A wheelbarrow \(6.00 \mathrm{ft}\) long is used to haul a \(18 \overline{0}\) -lb load. (a) How far from the wheel is the load placed so that a person can lift the load with a force of \(45.0 \mathrm{lb}\) ? (b) Find the MA.

Can you arrange a pulley system containing 10 pulleys and obtain a mechanical advantage of \(12 ?\) Why or why not?