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Question:

On a bicycle there are 30 teeth on the gear sprocket connected to the pedals, and 10 teeth on the sprocket connected to the rear wheels. If you pedal the bike 12 times, how many times will the rear wheel turn?

A 36 times

explanation

Since there are 30 teeth on the pedal sprocket, but only 10 teeth on the rear wheel, each revolution of the pedal will turn the rear wheel 3 times. So 12 revolutions will turn the rear wheel 36 times.

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The well pictured above uses what type of simple machine to raise and lower a bucket?

Wheel and axle

The well pictured here uses a wheel and axle system. The movement at the wheel becomes smaller than the movement on the shaft, increasing the force on the shaft.

If a wedge is made longer relative to its height, how does the force increase?

The amount of lift is decreased as the wedge is moved horizontally.

When the distance of a lift is the same as the distance the initial force travels, the force in will equal the force out. Making the wedge longer relative to its height (less slope) will change this by decreasing the amount of lift that takes place as the wedge is moved horizontally.

When torque increases, speed ____.

increases

If you increase the torque you increase the speed UNLESS you increase the load.

An axe is an example of what type of simple machine.

Wedge

An axe is a classic example of a wedge.

What is a component of potential energy?

Gravity’s relationship to mass

An object’s potential energy is equal to its mass times its acceleration due to gravity times its height, or PE = mgh.

What is a vector quantity?

Gravity

Gravity is a type of force, and since force has magnitude and direction it is known as a vector quantity.

In the pulley system below, how fast does pulley D rotate, if pulley A rotates at 100 rpm?

12.5 rpm

A larger pulley causes a smaller pulley to rotate faster by the ratio of their diameters. If pulley A rotates at 100 rpm, then pulley B rotates at \(\frac{\mathrm{100 \times 4} }{\mathrm{10} } = 40\) rpm. Since C is directly connected to B it rotates at the same rate (40 rpm). Finally, pulley D will rotate at \(40 \times \frac{\mathrm{5} }{\mathrm{16} } = 12.5\) rpm

You’re using a 6-inch wrench to release the wheel nuts as you rotate your tires. If you’re applying 40 pounds of force, how much torque is on the wheel nut?

20 ft-lb

20 ft-lb. Torque equals pounds of force times feet in length 40 pounds of force times 1/2 foot equals 20 foot-pounds of torque.

How much force is needed to lift the 10kg weight?

5 kg

In a double-pulley system, the force is equal to the weight divided by two. It will require a 5 kg force to lift a 10kg weight.

Torque involves a perpendicular force applied to a lever arm that moves around a center of rotation. Increasing the length of the lever arm will do which of the following?

increase torque

Torque measures force applied during rotation: τ = rF. Torque (τ, the Greek letter tau) = the radius of the lever arm (r) multiplied by the force (F) applied. Radius is measured from the center of rotation or fulcrum to the point at which the perpendicular force is being applied. The resulting unit for torque is newton-meter (N-m) or foot-pound (ft-lb).

At minimum, how many pulleys are there in a block and tackle system?

Two

The block and tackle pulley system requires at least two or more pulleys. The bare minimum for this system is two.

A fish tank at an aquarium contains several cubic feet of water (1 cubic foot of water = 62.5 pounds). If the fish tank is 6 feet deep, 12 feet wide, and 13 feet long, what’s the approximate pressure at the bottom of the tank in pounds per square inch?

2.5

To find the pressure (psi), we must divide the tank’s total volume by the surface area of the bottom of the tank. The volume = 6 × 12 × 13 = 936 feet. Multiply it by 62.5 to convert it into pounds: 936 × 62.5 = 58,500. The bottom of the tank’s surface area is
12 ft × 13 ft = 144 inches × 156 inches.
Since pressure is in pounds per square inch (psi), we have to convert to inches. The surface area is 22,464 inches. The psi is 58,500 ÷ 22,464 which is approximately 2.6. The closest answer is 2.5.

A block of steel has a density of 0.29 pounds per cubic inch. If the block has dimensions of 1 inch by 1 inch by 3 inches, what is its weight?

0.87 pounds

The volume of the block can be calculated by multiplying its length by its width by its height, or 1 times 1 times 3, which equals 3 cubic inches. The weight is the density multiplied by its volume, which is 3 cubic inches multiplied by 0.29 pounds per cubic inch, which equals 0.87 pounds.

One horsepower is equivalent to ____.

746 watts

Horsepower is a unit used to rate internal combustion engines. One horsepower is the equivalent of 746 watts.