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Physics problems: conservation laws

Part 1

 

Problem 1.

If a 5 tons beam is raised 6 meters, what is it's potential energy? If it is raised another 8 meters in 6 seconds, what is the work done?

Solution

 

Problem 2.

(University Physics, 12th Edition, Young & Freedman 6.33) A 10-kg box moving at 5 m/s on a horizontal, frictionless surface runs into a light spring of force constant 100 N/cm. Use the work-energy theorem to find the maximum compression of the spring.

Solution

 

Problem 3.

A cat stuck up a tree and has 500 J gravitational potential energy. It then falls. Find the kinetic energy of the cat just before it is caught by the owner. Find the kinetic energy of the cat after it is caught by the owner. Find the wasted energy (after cat is caught by the owner).

Solution

 

Problem 4.

A 2000 kg truck is traveling east through an intersection at 2 m/s when it is hit simultaneously from the side and the rear. One car is a 1000 kg compact traveling north at 5 m/s.  The other car is a 1500 kg midsize traveling east at 10 m/s.  The three vehicles become entangled and slide at one body.  What are their speeds and direction just after the collision?

Solution

 

Problem 5.

A small body of mass is attached to a light thread which passes through a hole at the centre of a smooth table. The body is set into rotation in a circle of radius , with a speed of . The thread is then pulled down shortening the radius of the path to . What will the new linear speed and the new angular speed be?

Solution

 

 

 

 

 

Problem 6.

A metal surface is illuminated one by one by photons of energy 2 eV and 4 eV respectively. The work function of the metal is 0.5 eV. What is the ratio of the maximum speeds of electrons emitted in two cases?

Solution

 

Problem 7.

Ball A, with a mass of 2 kg, moves with a velocity 5 m/s. It collides with a stationary ball B, with a mass of 4 kg. After the collision, ball A moves in a direction 60.0 degrees to the left of its original direction, while ball B moves in a direction 50.0 degrees to the right of ball A's original direction. Calculate the velocities of each ball after the collision.

Solution

 

Problem 8.

A toy car 1 of mass 0.30 kg moves along a frictionless surface with a velocity of 0.20 m/s. It collides with another toy car 2, with a mass of 0.40 kg and a speed of 0.10 m/s in the same direction. After the collision, toy car 1 continues to move in the same direction with a velocity of 0.15 m/s. Calculate the speed of toy car 2 after the collision.

Solution

 

Problem 9.

A skater of mass 80 kg initially at rest speeds up to a final speed of 10.0 m/s along a straight line and towards the East direction.

(a) Find the momentum of the skater while at rest.

(b) Find the momentum of the skater while traveling with its final speed.

(c) Find the change in momentum of the skater.

(d) Find the impulse acted on the skater.

(e) If that impulse exerted on the skater acts for 4 s, find the average force acting on the skater.

Solution

 

Problem 10.

A constant force of 80 N acts for 8 s on a box of mass 10 kg horizontally that initially rests on a horizontal frictionless surface.

(a) Find the change in the box's momentum.

(b) Calculate the final speed of the box after the 8 s have passed.

Solution

 

 

 

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