$\mathbf{A}$ jet pilot takes his aircraft in a vertical loop (Fig. 5-43). Estimate the $78-\mathrm{kg}$ pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and $(c)$ at the top of the circle (assume the same speed).

A sports car crosses the bottom of a valley with a radius of curvature equal to $95 \mathrm{~m}$. At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

A jet pilot puts an aircraft with a constant speed into a vertical circular loop. (a) Which is greater, the normal force exerted on the seat by the pilot at the bottom of the loop or that at the top of the loop? Why? (b) If the speed of the aircraft is 700 km/h and the radius of the circle is 2.0 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. Express your answer in terms of the pilot's weight.

At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5-45) do not fall out? Assume a radius of curvature of $7.6 \mathrm{~m}$.

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

How last (in rpm) must a centrifuge rotate if a particle $8.00 \mathrm{~cm}$ from the axis of rotation is to experience an acceleration of $125,000 \mathrm{~g}^* \mathrm{~s}$ ?

A $1200$-kg car rounds a curve of radius $70$ m banked at an angle of $12\degree$. If the car is traveling at $90$ km/h, will a friction force be required? If so, how much and in what direction?

How many revolutions per minute would a 25-mdiameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point?

A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. How fast must the bucket move at the top of the circle so that the rope does not go slack?

In the figure below, the coefficient of static friction between mass ma and the table is 0.39, whereas the coefficient of kinetic friction is 0.30. What minimum value of ma will keep the system from starting to move? What value of ma will keep the system moving at a constant speed?

A child sitting $1.20 \mathrm{~m}$ from the centre of a merry-go-around moves with a speed of $1.30 \mathrm{~m} / \mathrm{~s}$. Estimate the net horizontal force exerted on the child (mass $=22.5 \mathrm{~kg}$ ).

A child sitting $1.20 \mathrm{~m}$ from the centre of a merry-go-around moves with a speed of $1.30 \mathrm{~m} / \mathrm{~s}$. Estimate the centripetal acceleration of the child

Suppose the coefficient of kinetic friction between the block and the plane in above question is $0.275$ . What would be the net work done in this case?

What is the maximum speed with which a $1200-\mathrm{~kg}$ car can round a turn of radius $80.0 \mathrm{~m}$ on a flat road if the coefficient of friction between tires and road is $0.65$ ? Is this result independent of the mass of the car?