1.1. A mass M of 2.71 kg is attached to the end of a string whose length is 0.370 m. The mass slides without friction on a horizontal surface. If the string can withstand a maximum tension of 64.5 N, what is the maximum tangential speed the ball can have before the cord breaks?

1.2. The same mass, with a new string, is whirled in a vertical circle of the same radius about a fixed point. Find the magnitude of the tension when the mass is at the top if its speed at the top is 7.17 m/s.

2.Highways are banked at an angle for a design speed at which friction is not required to steer the car around the curve. If the design speed is 62 mph, and the banking angle is 34 degrees, what is the radius of the curve in meters?

3. A steel ball of mass 1.17 kg is attached to a thin (massless) cable and whirled around in a circle in a vertical plane.The circle has a radius of 1.14 m. When it is at the bottom of the circle, the ball has a speed of 11.1 m/s. Calculate the magnitude of the tension in the cable when the mass is at the bottom of the circle.

4. A mass of 8.70 kg is suspended from a 1.23 m long string. It revolves in a horizontal circle. The tangential speed of the mass is 2.66 m/s. Calculate the angle between the string and the vertical.

5. Find the speed of a satellite in a circular orbit around the Earth with a radius 3.65 times the mean radius of the Earth; RE= 6.3710^3 km ME= 5.9810^24 kg

6. M1 is a spherical mass (37.0 kg) at the origin. M2 is also a spherical mass (17.8 kg) and is located on the x-axis at x = 65.4 m. At what value of x would a third mass with a 20.0 kg mass experience no net gravitational force due to M1 and M2?

7.1. Calculate the magnitude of the gravitational force between the earth and a 4.7 kg mass on the surface of the earth. The distance to the center of the earth from the surface is 6370 km and the mass of the earth is 5.9810^24.

7.2. Calculate the magnitude of the gravitational force between the moon and a 4.7 kg mass on the surface of the earth nearest to the moon. The distance to the center of the moon from the surface of the earth is 376,000 km and the mass of the moon is 7.3610^22 kg.

7.3. Calculate the ratio of the magnitude of the gravitational force between a 4.7 kg mass on the surface of the earth due to the sun to that due to the moon. The mass of the sun is 1.9910^30 kg and the distance from the center of the sun to the surface of the earth is 1.5010^8 km.