A 2kilogram block is released from rest at the top of a curved incline in the shape of a quarter of a circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless, but there is an 8newton force of friction on the block while it slides horizontally. Assume g = 10 meters per second2.
a. Determine the magnitude of the acceleration of the block while it slides along the horizontal plane.
b. What time elapses while the block is sliding horizontally?
c. Calculate the radius of the incline in meters.
1997 B1 - Homework
A 0.20 kg object moves along a straight line. The net force acting on the object varies with the object's displacement as shown in the graph above. The object starts from rest at displacement x = 0 and time t = 0 and is displaced a distance of 20 m. Determine each of the following.
a. The acceleration of the particle when its displacement x is 6 m.
b. The time taken for the object to be displaced the first 12 m.
c. The amount of work done by the net force in displacing the object the first 12 m.
d. The speed of the object at displacement x = 12 m.
e. The final speed of the object at displacement x = 20 m.
f. The change in the momentum of the object as it is displaced from x = 12 m to x = 20 m
1979 B1 - Homework
From the top of a cliff 80 meters high, a ball of mass 0.4 kilogram is launched horizontally with a velocity of 30 meters per second at time t = 0 as shown above. The potential energy of the ball is zero at the bottom of the cliff. Use g = 10 meters per second squared. a. Calculate the potential, kinetic, and focal energies of the ball at time t = O.
b. On the axes below, sketch and Label graphs of the potential, kinetic, and total energies of the ball as functions of the distance fallen from the top of the cliff cliff
c. On the axes below sketch and label the kinetic and potential energies of the ball as functions of time until the ball hits
1981 B2 - Class
A massless spring is between a 1kilogram mass and a 3kilogram mass as shown above, but is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1kilogram mass is held in place and the spring is compressed by pushing on the 3kilogram mass. The 3kilogram mass is then released and moves off with a speed of 10 meters per second.
a. Determine the minimum work needed to compress the spring in this experiment.
The spring is compressed again exactly as above, but this time both masses are released simultaneously.
b. Determine the final velocity of each mass relative to the cable after the masses are released.
1985 B1 - Class
A 2kilogram block initially hangs at rest at the end of two 1meter strings of negligible mass as shown on the left diagram above. A 0.003kilogram bullet, moving horizontally with a speed of 1000 meters per second, strikes the block and becomes embedded in it. After the collision, the bullet/ block combination swings upward, but does not rotate.
a. Calculate the speed v of the bullet/ block combination just after the collision.
b. Calculate the ratio of the initial kinetic energy of the bullet to the kinetic energy of the bullet/ block combination immediately after the collision.
c. Calculate the maximum vertical height above the initial rest position reached by the bullet/block combination.
1988 B2 - Class
A ball thrown vertically downward strikes a horizontal surface with a speed of 15 meters per second. It then bounces, and reaches a maximum height of 5 meters. Neglect air resistance on the ball.
a. What is the speed of the ball immediately after it rebounds from the surface?
b. What fraction of the ball's initial kinetic energy is apparently lost during the bounce?