Physics

A ball travels on a frictionless circular track at 3m/s. The ball cannot have an acceleration greater than 1.5m/s² or it will go off the track. What is the smallest radius the circular track can have so that the ball stays on the track?

A 3kg rock spins horizontally at the end of a 2m string at 90 RPM. Calculate its centripetal acceleration.

A small 4kg block is tied to the end of 3m string and slides around in a circle on a frictionless table. Suppose the string will break if the tension exceeds 50N. Find the maximum speed the block can have without breaking the string.

Suppose a 1,800-kg car passes over a bump in a roadway that follows the arc of a circle of radius 20m. What
force does the road exert on the car as the car moves over the top of the bump if the car moves at a constant 9 m/s?

A bobsled turn banked at 78° is taken at 24 m/s. Assume it is ideally banked and there is no friction between the ice and the bobsled. Calculate the centripetal acceleration of the bobsled.

Two spheres of mass 300 kg and 500 kg are placed in a line 20 cm apart. If another sphere of mass 200 kg is placed between them, 8 cm from the 300 kg sphere, what is the net gravitational force on the 200 kg sphere?

A 2,000-kg spacecraft is blasting away from the surface of an unknown planet the same size as the Earth. At 1500km above the surface, an instrument onboard reads the gravitational force to be 18000 N. What is the planet’s mass?

Find the magnitude & direction of the net gravitational force on the center 5-kg mass in the rectangle below.

You stand on the surface of a mysterious planet with a mass of 6×10²⁴kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?

How far would you have to be above Earth’s surface for g to be ½ of its surface value?

Suppose that you used some geometry and kinematics to estimate that the Earth goes around the Sun with an orbital speed of approximately 30,000 m/s (60,000 mph), and that the Sun is approximately 150 million kilometers away from the Earth. Use this information to estimate the mass of the Sun.

You throw a baseball horizontally while on the surface of a small, spherical asteroid of mass 7×10¹⁶ kg and diameter of 22km. What is the minimum speed so that it just barely goes around the asteroid without hitting anything?

A satellite orbits at an orbital period of 2 hours around the Moon. What is the satellite’s orbital altitude?

A distant planet orbits a star 3 times the mass of our Sun. This planet of mass 8×10²⁶ kg feels a gravitational force of 2×10²⁶ N. What is this planet’s orbital speed and how long does it take to orbit once?

You're on a satellite orbiting an unknown planet. The only property of this planet that you know is that days are 18 hours long. Your onboard sensors show that you're orbiting at 16,000 km above the surface, with a velocity of 3 km/s. You look down and notice that you're always above the same point on that planet as you orbit around it.
Calculate the mass of the planet.

Pluto's orbit is the most eccentric of the 9 large objects in our solar system, with e = 0.25. The total distance from Pluto’s closest to farthest point from the Sun is 1.18×10¹³m. a) How close does it get to the Sun? b) How far does it get from the Sun?

Io and Ganymede are two of Jupiter’s four Galilean moons. Io orbits at an average distance of 422,000km in 1.77 days. What is Ganymede’s average orbital distance (in km), if it takes 4 times longer to orbit Jupiter?