Exam 6: Gravity

In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km?

The reason an astronaut in an earth satellite feels weightless is that

A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is $13.2 \mathrm {~m}$ with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve?

Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7.0 times his true weight?

When an object moves in uniform circular motion, the direction of its acceleration is

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to be 25°?

A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a) What banking angle should you specify for this curve? (b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed?

The mass of Pluto is 1.31 × 10²² kg and its radius is 1.15 × 10⁶ m. What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along the line connecting A and B. When the third mass is suddenly released, find the magnitude and direction (toward A or toward B) of its initial acceleration. (G = 6.67 × 10^-11 N ∙ m²/kg²)

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 10²² kg, the distance to the Moon is 3.82 × 10⁸ m, and G = 6.67 × 10^-11 N ∙ m²/kg².

The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway?

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding?

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If g_m is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the location of the satellite?