A roller-coaster car at an amusement park has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, assume that its speed is not changing. At the top of the hill, what are the (a) magnitude

$$F_N$$

and (b) direction (up or down) of the normal force on the car from the track if the car’s speed is ν = 11 m/s? What are (c)

$$F_N$$

and (d) the direction if ν = 14 m/s?

A gyroscope flywheel of radius $2.83 \text{~cm}$ is accelerated from rest at $14.2\text{~ rad/s}^2$ until its angular speed is $2760\text{~ rev/min}$. Through what distance does a point on the rim move during the spin-up?

When the 5 -kg box reaches point A it has a speed $v_{A}=10$ m/s. Determine how high the box reaches up the surface before it comes to a stop. Also, what is the resultant normal force on the surface at this point and the acceleration? Neglect friction and the size of the box.

Motive power for the experimental 10-Mg bus comes from the energy stored in a rotating flywheel which it carries. The flywheel has a mass of 1500 kg and a radius of gyration of 500 mm and is brought up to a maximum speed of 4000 rev/min. If the bus starts from rest and acquires a speed of 72 km/h at the top of a hill 20 m above the starting position, compute the reduced speed N of the flywheel. Assume that 10 percent of the energy taken from the flywheel is lost. Neglect the rotational energy of the wheels of the bus. The 10-Mg mass includes the flywheel.

A 60-kg housepainter stands on a 15-kg aluminum platform. The platform is attached to a rope that passes through an overhead pulley, which allows the painter to raise herself and the platform (Figure 4-57).

$(b)$ When her speed reaches $1.0 \mathrm{~m} / \mathrm{s}$, she pulls in such a way that she and the platform go up at a constant speed. What force is she exerting on the rope now? (Ignore the mass of the rope.)

A speeding motorcyclist is traveling at a constant speed of $36.0 \mathrm{~m} / \mathrm{s}$ when he passes a police car parked on the side of the road. The radar, positioned in the police car's rear window, measures the speed of the motorcycle. At the instant the motorcycle passes the police car, the police officer starts to chase the motorcyclist with a constant acceleration of $4.0 \mathrm{~m} / \mathrm{s}^2$. a) How long will it take the police officer to catch the motorcyclist? b) What is the speed of the police car when it catches up to the motorcycle? c) How far will the police car be from its original position?

If the thermal (incoherent kinetic) energy of a system made up of 1.00 mol of argon atoms ($6.02 \times 10 ^ { 23 }$ atoms) is 498 J, what is the average speed of each atom? The mass of an argon atom is $6.63 \times 10 ^ { - 26 } \mathrm { kg }$.

A gyroscope flywheel of radius $2.83 \text{~cm}$ is accelerated from rest at $14.2\text{~ rad/s}^2$ until its angular speed is $2760\text{~ rev/min}$. What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process?

You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height $h$, or (b) pull it up a long, frictionless plane inclined at a $15^{\circ}$ angle until its height has increased by $h$. Assume you will move the block at constant speed either way. Will you do more work in case a or case b? Or is the work the same in both cases? Explain.

A projectile is fired up an incline (incline angle $\phi$) with an initial speed vi at an angle $\theta$i with respect to the horizontal ($( \theta i > \phi )$). (a) Show that the projectile travels a distance d up the incline, where(b) For what value of $\theta$i is d a maximum, and what is that maximum value? $d = \frac { 2 v _ { i } ^ { 2 } \cos \theta _ { i } \sin \left( \theta _ { i } - \phi \right) } { g \cos ^ { 2 } \phi }$

A 71 kg baseball player jumps straight up to catch a hard-hit ball. If the 140 g ball is moving horizontally at 28 m/s, and the catch is made when the ballplayer is at the highest point of his leap, what is his speed immediately after stopping the ball?

The absolute temperature of gas doubled, what happens to the root-mean-square speed of the molecules?

A) Nothing happens to the rms speed
B) The new rms speed = $4$ times the original rms speed
C) The new rms speed = $2$ times the original rms speed
D) The new speed is $1.414$ times the original rms speed
E) The new speed is $1/2$ the original rms speed

One of the events in the Scottish Highland Games is the sheaf toss, in which a $9.09-\mathrm{kg}$ bag of hay is tossed straight up into the air using a pitchfork. During one throw, the sheaf is launched straight up with an initial speed of $2.70 \mathrm{~m} / \mathrm{s}$. b) Neglecting air resistance, what is the impulse exerted by gravity on the sheaf during its downward motion (from maximum height until it hits the ground)?

A policeman starts giving chase 60 seconds after a stolen car zooms by at 108 km/hr. At what minimum speed should he drive if he has to catch up with the driver before he manages to get onto an expressway 60 km away?