5277

Mathematics Integration Level: Misc Level

Evaluate the following definite integral

\int_{0}^{1}\sqrt{5x+4}dx




5276

Mathematics Integration Level: Misc Level

Evaluate the following definite integral

\int_{2}^{3}\frac{1}{x}dx




5275

Physics Force & Laws Of Motion Level: Misc Level

A bullet, of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30 % with the plane of the plate. It ricochets off at the same angle ,at a speed of 320 m/s. What is the magnitude of the impulse that the wall gives to the bullet?

(a) 0.30 N s

(b) 300 N s

(c) 0.52 N s

(d) 6.7 N s

 

 

(c) 0.52 N s




5274

Physics Kinematics Level: Misc Level

A plane, flying horizontally, releases a bomb, which explodes before hitting the ground. Neglecting air resistance, the center of mass of the bomb fragments, just after the explosion 

(a) is zero

(b) moves along a parabolic path

(c) moves vertically

(d) moves horizontally




5273

Physics Force & Laws Of Motion Level: Misc Level

Two cars suffer a head -on collision. What is conserved in the collision?

(a) none of these

(b) kinetic energy

(c) momentum

(d) mechanical energy and momentum




5272

Physics Work,Power & Energy Level: Misc Level

How fast must a 10.5 g bullet be traveling when it strikes a ballistic pendulum that consists of a block of wood of mass 3.0 kg that is suspended by a cord? The bullet gets embedded in the block. The block rises by 0.22 m after the impact.




5271

Physics Force & Laws Of Motion Level: Misc Level

The momentum of a particle is proportional to the square of its velocity.

(a) Ttue

(b) False




5270

Physics Work,Power & Energy Level: Misc Level

Approximately what running speed would an 80 kg polevaulter have to acquire to clear a bar 5.0 m off the ground? Assume that the pole- vaulter,s center of gravity is initially 1.0 m off the ground and that the vaulter clears the bar if his center of gravity just reaches the height of the bar.




5269

Physics Work,Power & Energy Level: Misc Level

(a) A spring is hung from a ceiling  and a 500 g mass is hung from it. This increases the length of the spring by 20.0 cm. what is the force constant k for the spring?

(b) If the same spring is then moved from the ceiling to a wail and stretched horizontally so that the 500 g mass is displaced 40.0 cm from its equilibrium position, what is the stored potential energy in the spring?




5267

Physics Work,Power & Energy Level: Misc Level

A workman pushes a 200 kg crate up a frictionless meetal ramp of length 4.00 m into the back of a truck (See figure below).

(a) If the angle made by the ramp with the ground is 25.0 degrees and the workman pushes the block at a very slow, constant speed, how much work does he do?

(b) what is the increased gravitational potential energy of the crate




5266

Physics Work,Power & Energy Level: Misc Level

A 100 kg man pulls his 30.0 kg daughter on a sled with a rope that makes an angle of 40.0 degrees with respect to the ground.

(a) If the man exerts a force of 50.0 N and the sled moves 100 m, how much work does he do?

(b) If the man pulls horizontaliy on the sled, what force would he have to exert to do the same amount of work?




5265

Physics Kinematics Level: Misc Level

A 60 kg woman pushes a 20 kg suitcase on wheels a distance of 10 m by exerting a force of 2.0 N in the direction of motion, starting from (a) How much work does she do? (b) If there were no friction acting on the suitcase, what would its final velocity be at the end of the 10 m distance?




5264

Physics Rotational Mechanics Level: Misc Level

Three masses are positioned at the following coordinates :3.0 kg at ( 3,2) : 4.0 kg at (0,1) :and  5.0 kg at ( 5,-7). what are the coordinates of the center of mass of this system?




5262

Physics Force & Laws Of Motion Level: Misc Level

A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. Ifthe cars lock together as a result of the collision,what is their common speed afterward?




5261

Physics Work,Power & Energy Level: Misc Level

Lisa runs up 4 flights of stairs in 22 s. She weighs 510 N. If each flight rises 310 cm:

(a) What is her change in potential?

(b) What average power ( watts ) was required during the 22 s?

(c) What minimum horsepower motor would be required to do this?


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