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A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadwayaround a right turn radius of 30.0 m before the cup starts toslide? If you go too fast, in what direction will the cupslide relative to the dashboard?

The spring in the figure (a) is compressed by length delta x . It launches the block across a frictionless surface with speed v0. The two springs in the figure (b) are identical to the spring of the figure (a). They are compressed by the same length delta x and used to launch the same block. What is the block's speed now?

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.

A 5.00 kg package slides 1.50 m down a long ramp that is inclined at ${\displaystyle {12.0}^{\circ }}$ below the horizontal. The coefficient of kinetic friction between the package and the ramp is k =0.310. Calculate 
(a) the work done on the package by friction (b) the workdone on the package by gravity (c) the work done on the package bythe normal force (d) the total work done on the package (e) Ifthe package has a speed of 2.20 m/s at the top of the ramp, what isits speed after sliding 1.50 m down the ramp?

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds $4.50\cdot {10}^4$N and our hero's mass is 86.5 kg.

 Figure 1 a) If the angle $\theta$ is ${13.0}^{\circ }$, find the tension iin the rope.

b) What is the smallest value the angle $\theta$ can have if the rope is not to break?

The end of the cutting cord on a gas-powered weed cutter is0.15 m in length. If the motor rotates at the rate of 20rev/s, what is the tangential sped of the end of the cord? 
a) 628 m/s 
b) 25 m/s 
c) 19 m/s 
d) 63 m/s 
e) 75 m/s

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of ${\displaystyle 1950N\cdot m}$ to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

The rotor (flywheel) of a toy gyroscope hasmass 0.140 kg. Its moment of inertia about its axis is . The mass of the frame is 0.0250 kg. The gyroscopeis supported on a single pivot javascript:void(0); with its center of mass a horizontaldistance of 4.00 cm from the pivot. The gyroscope is precessing ina horizontal plane at the rate of one revolution in 2.20 s. Find the upward force exerted by thepivot. Find the angular speed with which the rotoris spinning about its axis, expressed in rev/min. Comments

A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s a long its initial line of motion with an acceleration of 30.0 m/s/s. At this time, its engines fail and the rocket proceeds to move as a projectile. Find: 
a) the maximum altitude reached by the rocket 
b) its total time of flight 
c) its horizontal range.

A skier of mass 70 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s ?(b) What power must a motor have to perform this task?

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes. Find the tension in each rope when a 700-N person is 0.500 m from the left end.

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables.Because the ceiling is covered with intricate architectur al decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension ${\displaystyle T_1}$ and makes an angle of ${\displaystyle {\theta }_1}$ with the ceiling. Cable 2 has tension ${\displaystyle T_2}$ and makes an angle of ${\displaystyle {\theta }_2}$ with the ceiling.
Find an expression for ${\displaystyle T_1}$, the tension in cable 1, that does not depend on ${\displaystyle T_2}$.
Express your answer in terms of someor all of the variables m,${\displaystyle {\theta }_1}$, and ${\displaystyle {\theta }_2}$, as well as the magnitude of the acceleration due to gravity g.

A 0.450 kg ice puck, moving east with a speed of ${\displaystyle 3.00\frac{m}{s}}$ has a head in collision with a 0.900 kg puck, initially at rest. Assuming a perfectly elastic collision what will be the speed and direction of each object after the collision?

The specific gravity of ice is 0.917, whereas that for seawater is 1.025. What fraction of an iceberg is above the surface of the water?

A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible. 
a) What is the speed of the rock when the string passesthrough the vertical position? 
b) What is the tension in the string when it makes an angle of 45 with the vertical? 
c) What is the tension in the string as it passes through the vertical? 
 

A point charge has a charge of 2.50x10-11C. Atwhat distance from the point charge is the electric potential a)90.0V? b) 30.0V? Take the potential to be zero at an infinitedistance from the charge.

A block is hung by a string from inside the roof of avan. When the van goes straight ahead at a speed of 24 m/s,the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 175m) the block swings toward the outside of the curve, then the string makes an angle theta with the vertical. Find theta.

A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g Ping Pong ball move so that the two balls have the same kinetic energy?

A sled with rider having a combined mass of 120 kg travels over the perfectly smooth icy hill shown in the accompanying figure. How far does the sled land from the foot of the cliff (in m)?