Example #1: Push-Away With Energy

Practice: Two blocks (3 kg and 4 kg) on a smooth floor are pressed against a light spring (force constant 800 N/m) between them. When the blocks are released, the 3 kg is launched with 10 m/s.

(a) What speed is the 4 kg launched with?

(b) How much was the spring compressed by before the blocks were released?

Blocks A and B are initially at rest on a horizontal frictionless surface with a spring of negligible mass compressed between them. Block A has mass 5.0 kg and block B has mass 20.0 kg. The spring is released and the blocks move off in opposite directions. After the blocks, have moved away from the spring.
A) the magnitude of the momentum of block A is the same as the magnitude of the momentum of block B
B) the magnitude of the momentum of block A is less than the magnitude of the momentum of block B
C) the magnitude of the momentum of block A is greater than the magnitude of the momentum of block B

Two blocks are at rest on a horizontal frictionless surface with a compressed spring of negligible mass between them. Block A has mass 2.00 kg and block B has mass 5.00 kg. The blocks are released from rest and move off in opposite directions, leaving the spring behind. If block B has speed 0.800 m/s after it leaves the spring, what is the speed of block A after it leaves the spring? (Block A is the less massive block.)
(a) 0.63 m/s
(b) 0.95 m/s
(c) 1.00 m/s
(d) 1.26 m/s
(e) 1.50 m/s
(f) 2.00 m/s
(g) none of the above answers

A 20.0-kg projectile is fired at an angle of 60.0° above the horizontal with a speed of 80.0 m/s{
m{ m/s}}. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance.(a) How far from the point of firing does the other fragment strike if the terrain is level?(b) How much energy is released during the explosion?

A 140 kg astronaut (including space suit) acquires a speed of 2.60m/s by pushing off with his legs from a 1800 kg space capsule.(a) What is the change in speed of the space capsule?(b) If the push lasts 0.505 s, what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push.(c) What is the kinetic energy of the astronaut after the push?(d) What is the kinetic energy of the space capsule after the push?

Boxes A and B are at rest on a horizontal frictionless surface with a compressed spring of negligible mass between them. Box a has mass 2.0 kg and box B has 4.0 kg. When the spring is released the two boxes move off in opposite direction and the spring is left behind. After the boxes have moved away from the spring,A) the magnitude of the momentum of A is less than the magnitude of the momentum of BB) the magnitude of the momentum of A is greater than the magnitude of the momentum of BC) the magnitude of the momentum of A is equals than the magnitude of the momentum of BD) the kinetic energy of A equals the kinetic energy of B

A 65.0-kg boy and his 40.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with velocity 2.90 m/s toward the west. Ignore friction.(a) Describe the subsequent motion of the girl.(b) How much potential energy in the girl’s body is converted into mechanical energy of the boy–girl system?

A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 X 104 N/m, as shown in the figure. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0° above the horizontal. Assuming that the mass of the cannon and its carriage is 5000 kg,(a) Find the recoil speed of the cannon.(b) Determine the maximum extension of the spring.(c) Find the maximum force the spring exerts on the carriage.(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?

Old naval ships fired 13 kg cannon balls from a 230 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 2.5×104 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ships frame. What was the speed of the cannon ball if the spring compressed 56 cm when the cannon was fired?

An atomic nucleus at rest decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is 2.6×105 m/s? Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.

A 8.50 kg shell at rest explodes into two fragments, one with a mass of 2.50 kg and the other with a mass of 6.00 kg. If the heavier fragment gains 130 J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?

An atomic nucleus initially moving at 435 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 216 u , what speed does the alpha particle have when it is emitted?

A 226-kg projectile, fired with a speed of 126 m/s at a 61.0 angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally.(a) Determine the magnitude of the velocity of the third fragment immediately after the explosion.(b) Determine the direction of the velocity of the third fragment immediately after the explosion.(c) Determine the energy released in the explosion.

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.7 times the mass of the other. If 7300 J is released in the explosion, how much kinetic energy does each piece acquire?