An athlete in a gym applies a constant force of 50 N to the pedals of a bicycle to keep the rotation rate of the wheel at 10 rev/s. The length of the pedal arms is 30 cm. What is the power delivered to the bicycle by the athlete?

A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 3090 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean

$$\mu = 298 ml$$

and standard deviation

$$\sigma = 3 ml$$

. What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml? Show your work.

A flywheel (I = 50 kg-m²) starting from rest acquires an angular velocity of 200.0 rad/s while subject to a constant torque from a motor for 5 s. (a) What is the angular acceleration of the flywheel? (b) What is the magnitude of the torque?

A wind turbine rotates at 20 rev/min. If its power output is 2.0 MW, what is the torque produced on the turbine from the wind?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

$$\frac { 7 + 3 i } { 5 + 3 i } = \frac { 7 } { 5 }$$

At what point in the path of a projectile is the speed a minimum?

A uniform cylindrical grindstone has a mass of 10 kg and a radius of 12 cm. (a) What is the rotational kinetic energy of the grindstone when it is rotating at 1.5 × 10³ rev/min? (b) After the grindstone's motor is turned off, a knife blade is pressed against the outer edge of the grindstone with a perpendicular force of 5.0 N. The coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.

The cart shown below moves across the table top as the block falls. What is the acceleration of the cart? Neglect friction and assume the following data: $m_1=2.0 \mathrm{~kg}, m_2=4.0 \mathrm{~kg}, I=0.4 \mathrm{~kg}-\mathrm{m}^2, r=20 \mathrm{~cm}$

What force must be applied to end of a rod along the $x$-axis of length $2.0 \mathrm{~m}$ in order to produce a torque on the rod about the origin of $8.0 \hat{\mathbf{k}} \mathrm{N} \cdot \mathrm{m}$ ?

A gas has a volume of 450.0 mL. If the temperature is held constant, what volume would the gas occupy if the pressure were a. doubled? (Hint: Express

$$P_2$$

in terms of

$$P_1$$

.), b. reduced to one-fourth of its original value?

Convert each polar equation to a rectangular equation. $r=\frac{8}{2-\sin \theta}$

Complete the sentence. Through any _ noncollinear points, there exists exactly one plane.

Simplify. $\sqrt{108}$

A seesaw has length $10.0 \mathrm{~m}$ and uniform mass $10.0 \mathrm{~kg}$ and is resting at an angle of $30^{\circ}$ with respect to the ground (see the following figure). The pivot is located at $6.0 \mathrm{~m}$. What magnitude of force needs to be applied perpendicular to the seesaw at the raised end so as to allow the seesaw to barely start to rotate?