Classical Mechanics Answers

1. Ceres is the largest asteroid. Its mean radius is 476 km and its mass is 9.4×10^20 kg. Using this, and G = 6.67×10^−11 Nm^2 kg^−2, and approximating it as a sphere, compute the speed required to escape the gravity on the surface of Ceres.

Speed = ___ m.s^−1. (to two significant figures, don't use scientific notation)

2. Consider the mechanical energy of a body in geostationary orbit above the Earth's equator, at rGS = 42000.

Consider the mechanical energy of the same body on Earth at the South pole, at re = 6400 km. For this problem, we consider the Earth to be spherical. (Remember, the object at the equator is in orbit, the object at the Pole is not in orbit.)

G = 6.67×10^−11 Nm^2 kg^−2, and the mass of the Earth is M = 5.97×10^24 kg.

What is the difference in the mechanical energy per kilogram between the two?

E= ___ MJ.kg^−1 (to two significant figures, don't use scientific notation).

A rubber band has mass m = 0.30 g and a spring constant k = 15 N.m^−1 . I stretch it by 5.0 cm (which in this case doubles its length). Assume the rubber band behaves as a Hooke's law spring. Assume that, when you launch the rubber band, all of the stored potential energy is converted into kinetic energy. How fast is it at the launch?

v = _____ m.s^−1 . ( USE THE CORRECT SIGNIFICANT NUMBER FOR THE FINAL ANSWER)

1. The Earth is 8 light minutes from the sun and the speed of light is 3×10^8 m.s^−1. Let's assume that earth's orbit is exactly circular. Its mass is 5.972×10^24 kg.

Using the values given above (and your knowledge about time units), determine the magnitude of the gravitational force that the Sun exerts on the Earth.

The magnitude of the force is _____ newtons.

Format: if your answer is 2×10^3 N, enter 2*10^3 (and do think about significant figures).

A simple carousel consists of a flat circular floor that rotates about 12 seconds.

a) Calculate and illustrate all the forces acting on a person standing 4.5 m from the center of the carousel. The person weighs 55 kg.

b) What is the shortest lap time the carousel can have without the person starting to slip? The friction number between the person's shoes and the floor is 0.45.

A novice golfer on the green takes three strokes to sink the ball .The successive displacement of the ball are 4.00 m to the north 2.00 m northwest and 1.00 m at 30.0 west of south .starting at the same initial point an expert golfer could make the hole in which single displacement.

A spring is kept caught by a thread.In one moment we burn the thread and the object flies with the speed of V1=10m/s.If μ=0.01 find the distance of the road made by the carriage until it stops.Mass of the carriage=1kg,mass of the object=0.1kg.

i got 2 questions. One motions one Newton’s Law

Q1) Object A is dropped from height h.At the same instant object B is thrown vertically upwards from the ground. Right before they collide in mid-air, the speed of A is twice of the speed of B. Determine the height h of collision

Q2) The pages of 2 identical books A and B are overlapping on one and another. The mass of each book is 1000g and the number of pages is \mu =0.3 . Book A is fixed on the table which a horizontal force F is pulling book B. Determine the minimum value of F to pull book B out.

A flywheel mounted on a shaft of radius 2 cm has a moment of inertia 1.6*10^-3 kg m^2. A string of length 2 m and with a mass of 1 kg is wound on the shaft and is let to fall down. The mass takes 10 s to get off the shaft's pin. Find the work done per revolution.

An observer finds that 20cm is the least distance from his eye at which he can place a convex mirror of focal length 15cm in order to see his own eye clearly. What is his least distance of distinct vision?

Ceres is the largest asteroid. Its mean radius is }476 km and its mass is 9.4×10^20 kg. Using this, and G = 6.67×10^ −11 Nm^2 kg^ −2, and approximating it as a sphere, compute the speed required to escape the gravity on the surface of Ceres.

Speed= ___ m/s . (to two significant figures, don't use scientific notation)