1. A battleship that is 8.00 ✕ 107 kg and is originally at rest fires a 900–kg artillery shell horizontally with a veloc
Posted: Sat Jul 02, 2022 7:36 pm
1.
A battleship thatis 8.00 ✕ 107 kg and is originallyat rest fires a 900–kg artillery shell horizontally witha velocity of 600 m/s.
(a)
If the shell is fired straight aft (toward the rear of theship), there will be negligible friction opposing the ship'srecoil. Calculate its recoil velocity in meters per second.
(b)
Calculate the increase in internal kinetic energy in joules(that is, for the ship and the shell). This energy is less than theenergy released by the gun powder — significant heattransfer occurs.
2. Two manned satellites approach one another at a relativespeed of 0.200 m/s, intending to dock. The first has amass of 3.50 ✕ 103 kg, and thesecond a massof 7.50 ✕ 103 kg. If the twosatellites collide elastically rather than dock, what is theirfinal relative velocity in meters per second? (Adopt the referenceframe in which the second satellite is initially at rest and assumethat the positive direction is directed from the second satellitetowards the first satellite.)
3.
A 3500 kg cannon is mounted so that it can recoil onlyin the horizontal direction.
(a)
Calculate its recoil velocity in m/s when it firesa 15.0 kg shell at 480 m/s at an angle of20.0° above the horizontal. (Enter the magnitude.)
m/s
(b)
What is the kinetic energy of the cannon in J? This energy isdissipated as heat transfer in shock absorbers that stop itsrecoil.
J
(c)
What happens to the vertical component of momentum that isimparted to the cannon when it is fired?
4.
Two cars collide at an icy intersection and stick togetherafterward. The first car has a mass of 1650 kg and wasapproaching at 5.00 m/s due south. The second carhas a mass of 800 kg and was approachingat 25.0 m/s due west.
(a)
Calculate the final velocity (magnitude in m/s and direction indegrees counterclockwise from the west) of the cars. (Note thatsince both cars have an initial velocity, you cannot use theequations for conservation of momentum alongthe x-axis and y-axis; instead,you must look for other simplifying aspects.)
magnitude m/sdirection ° counterclockwise fromwest
(b)
How much kinetic energy (in J) is lost in the collision? (Thisenergy goes into deformation of the cars.)
J
A battleship thatis 8.00 ✕ 107 kg and is originallyat rest fires a 900–kg artillery shell horizontally witha velocity of 600 m/s.
(a)
If the shell is fired straight aft (toward the rear of theship), there will be negligible friction opposing the ship'srecoil. Calculate its recoil velocity in meters per second.
(b)
Calculate the increase in internal kinetic energy in joules(that is, for the ship and the shell). This energy is less than theenergy released by the gun powder — significant heattransfer occurs.
2. Two manned satellites approach one another at a relativespeed of 0.200 m/s, intending to dock. The first has amass of 3.50 ✕ 103 kg, and thesecond a massof 7.50 ✕ 103 kg. If the twosatellites collide elastically rather than dock, what is theirfinal relative velocity in meters per second? (Adopt the referenceframe in which the second satellite is initially at rest and assumethat the positive direction is directed from the second satellitetowards the first satellite.)
3.
A 3500 kg cannon is mounted so that it can recoil onlyin the horizontal direction.
(a)
Calculate its recoil velocity in m/s when it firesa 15.0 kg shell at 480 m/s at an angle of20.0° above the horizontal. (Enter the magnitude.)
m/s
(b)
What is the kinetic energy of the cannon in J? This energy isdissipated as heat transfer in shock absorbers that stop itsrecoil.
J
(c)
What happens to the vertical component of momentum that isimparted to the cannon when it is fired?
4.
Two cars collide at an icy intersection and stick togetherafterward. The first car has a mass of 1650 kg and wasapproaching at 5.00 m/s due south. The second carhas a mass of 800 kg and was approachingat 25.0 m/s due west.
(a)
Calculate the final velocity (magnitude in m/s and direction indegrees counterclockwise from the west) of the cars. (Note thatsince both cars have an initial velocity, you cannot use theequations for conservation of momentum alongthe x-axis and y-axis; instead,you must look for other simplifying aspects.)
magnitude m/sdirection ° counterclockwise fromwest
(b)
How much kinetic energy (in J) is lost in the collision? (Thisenergy goes into deformation of the cars.)
J