Classical Mechanics Answers

The final answer should be in the format of "tolerance of ± in the third significant digit.

1.The drag racer P starts from rest at the start line S and then accelerates along the track. When it has traveled 102 m, its speed is 51 m/s. For that instant, determine the values of r˙ and θ˙ relative to axes fixed to an observer O in the grandstand G as shown.

28 meters from point O ( it is the base of the triangle)

r˙ = ___ m/s

θ˙ = ____ rad/s

The final answer should be in the format of "tolerance of ± in the third significant digit."

A particle moving in the x-y plane has a position vector given by r = 2.26t²i + 1.22t³j, where r is in inches and t is in seconds. Calculate the radius of curvature ρ of the path for the position of the particle when t = 2.0 sec. Sketch the velocity v and the curvature of the path for this particular instant.

ρ = ______ in.

A small particle P starts from point O with a negligible speed and increases its speed to a value v = square root of 2gy, where y is the vertical drop from O. When x = 57 ft, determine the n-component of acceleration of the particle.

y = (x/15)² ft

a_n = _______ ft/sec²

The final answer should be in the format of "tolerance of ± in the third significant digit."

The car is traveling at a speed of 69 mi/hr as it approaches point A. Beginning at A, the car decelerates at a constant 6.9 ft/sec² until it gets to point B, after which its constant rate of decrease of speed is 2.0 ft/sec² as it rounds the interchange ramp. Determine the magnitude of the total car acceleration (a) just before it gets to B, (b) just after it passes B, and (c) at point C.

Distance from A to B is 325’

Radius is 243’

(a) Just before B,a = ________ ft/sec²

(b) Just after B,a = ______ ft/sec²

(c) At C,a = _______  ft/sec²

The final answer should be in the format of "tolerance of ± in the third significant digit."

A car is traveling around a circular track of a 730-ft radius. If the magnitude of its total acceleration is 11 ft/sec² at the instant when its speed is 50 mi/hr, determine the rate a_t which the car is changing its speed.

a_t = ± _________ ft/sec²

Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 33° if θ˙ = 2.41 rad/sec and θ¨ = 4.445 rad/sec².

a = (_____ e_n + _____ e_t) ft/sec²

a = (_____ i + ______ j) ft/sec²

This "J" shaped object (mass 320 kg) is hung by 2 cables. What is the Tension in the cable on the RIGHT and the LEFT? What minimum force would cause this to tip?

 A 8.75- g bullet from a 9-mm pistol has a velocity of 397.0 m/s. It strikes the 0.705- kg block of a ballistic pendulum and passes completely through the block. If the block rises through a distance h = 21.83 cm, what was the velocity of the bullet as it emerged from the block?

two particles A and B, of masses 3m and 4m respectively, attached to the ends of a light inextensible string. Initially A is held at rest on the surface of a fixed rough inclined plane. The plane is inclined to the horizontal at an angle x where tan(x) = 3/4 . The coefficient of friction between A and the plane is 1/4 . The string passes over a small smooth light pulley P which is fixed at the top of the plane. The part of the string from A to P is parallel to a line of greatest slope of the plane. The particle B hangs freely and is vertically below P. The system is released from rest with the string taut and with B at a height of 1.75 m above the ground. In the subsequent motion, A does not hit the pulley.

When B hits the ground, B does not rebound and comes immediately to rest.

Find the distance travelled by A from the instant when the system is released to the instant when A first comes to rest.

Find the velocity V, the period T, of a conical pendulum of mass M attached to a string of length L making angle teta with vertical

A 500-kg satellite is in a circular orbit at an altitude of 500 km above the Earth’s surface. Because of air friction, the satellite eventually falls to the Earth’s surface, where it hits the ground with a speed of 2.00 km/s. How much energy was transformed into internal energy by means of air friction?

If you plot the one-dimensional displacement of an object as a function of time making an x-t curve, then the acceleration at a point on the curve is 

given by the slope at that point.

given by the curvature at that point.

positive if the curvature is upward.

negative if the curvature is upward.