A $1050 \mathrm{~kg}$ car rounds a curve of radius $72 \mathrm{~m}$ banked at an angle of $14^{\circ}$. If the car is traveling at $85 \mathrm{~km} / \mathrm{h}$, will a friction force be required? If so, how much and in what direction?

A car at the Indianapolis-$500$ accelerates uniformly from the pit area, going from rest to $320$ km/h in a semicircular arc with a radius of $200$ m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the roadbed to provide this acceleration with no slipping or skidding?

A $62-\mathrm{kg}$ skier starts from rest at the top of a ski jump, point $\mathrm{A}$ in given Fig, and travels down the ramp. If friction and air resistance can be neglected, find her speed $v_{\mathrm{B}}$ when she reaches the horizontal end of the ramp at B.

A $62-\mathrm{kg}$ skier starts from rest at the top of a ski jump, point $\mathrm{A}$ in given Fig., and travels down the ramp. If friction and air resistance can be neglected, find the distance $s$ to where she strikes the ground at $\mathrm{C}$

A device for training astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius $11.0 \mathrm{~m}$. If the force felt by a trainee is $7.45$ times her own weight, how fast is she revolving? Express your answer in both $\mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$.

What is the maximum speed with which a $1200$ kg car can round a turn of radius $75$ m on a flat road if the coefficient of static friction between tires and road is $0.80$? Is this result independent of the mass of the car?

A body with a mass of 10.0 kg is assumed to be in Earth's gravitational field with g = 9.80 m/s². What is its acceleration?

Consider a train that rounds a curve with a radius of $570 \mathrm{~m}$ at a speed of $160 \mathrm{~km} / \mathrm{h}$ (approximately $100 \mathrm{mi} / \mathrm{h}$ ). $(a)$ Calculate the friction force needed on a train passenger of mass $55 \mathrm{~kg}$ if the track is not banked and the train does not tilt. $(b)$ Calculate the friction force on the passenger if the train tilts at an angle of $8.0^{\circ}$ toward the center of the curve.

A device for training astronauts and jet fighter pilots is designed to rotate the trainee in a horizontal circle of radius $10.0$ m. If the force felt by the trainee is $7.75$ times her own weight, how fast is she rotating? Express your answer in both m/s and rev/s.

A roller coaster reaches the top of the steepest hill with a speed of 6.0 km/h. It then descends the hill, which is at an average angle of $45^{\circ}$ and is $45.0 \mathrm{m}$ long. Estimate its speed when it reaches the bottom. Assume $\mu_{\mathrm{k}}=0.18$.

A $28.0-\mathrm{~kg}$ block is connected to an empty $2.00-\mathrm{~kg}$ bucket by a cord running over a frictionless pulley (Fig. 5-52). The coefficient of static friction between the table and the block is $0.45$ and the coefficient of kinetic friction between the table and the block is $0.32$. Sand is gradually added to the bucket until the system just begins to move. Estimate the mass of sand added to the bucket.

Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan’s weight is 800 N, Jane’s weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and immediately jump off. Jonathan jumps to the left with a velocity of 5.00 m/s at $30.0^{\circ}$ above the horizontal (relative to the ice), and Jane jumps to the right at 7.00 m/s at $36.9^{\circ}$ above the horizontal (relative to the ice). Calculate the sleigh’s horizontal velocity (magnitude and direction) after they jump out.

A train traveling at a constant speed rounds a curve of radius $215 \mathrm{~m}$. A lamp suspended from the ceiling swings out to an angle of $18.5^{\circ}$ throughout the curve. What is the speed of the train?

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?