Part A-
1- You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 38 N•m. Using the data in the drawing, determine the magnitude F of the force that you must exert on the wrench.
2- A square, 0.80 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. The axis is perpendicular to the plane of the square. A force of 15.6 N lies in this plane and is applied to the square. What is the magnitude of the maximum torque that such a force could produce?
3- One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first force has a magnitude of 2.00 N and is applied perpendicular to the length of the stick at the free end. The second force has a magnitude of 6.00 N and acts at a 22.9° angle with respect to the length of the stick. Where along the stick is the 6.00-N force applied? Express this distance with respect to the end of the stick that is pinned.
4- The drawing shows a lower leg being exercised. It has a 53-N weight attached to the foot and is extended at an angle θ with respect to the vertical. Consider a rotational axis at the knee.
(a) When θ = 90.0°, find the magnitude of the torque that the weight creates.
N • m
(b) At what angle θ does the magnitude of the torque equal 15 N•m?
°
Part B-
1- The earth spins on its axis once a day and orbits the sun once a year (365.24 days). Take the positive direction for the angular displacement to be the direction of the earth's motion.
(a) Determine the average angular velocity of the earth as it spins on its axis.
rad/s
(b) Determine its angular velocity as it revolves around the sun.
rad/s
2- A pitcher throws a curveball that reaches the catcher in 0.69 s. The ball curves because it is spinning at an average angular velocity of 335 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?
radians
3- An electric circular saw is designed to reach its final angular speed, starting from rest, in 1.54 s. Its average angular acceleration is 360 rad/s2. Obtain its final angular speed.
rad/s
4- The angular speed of the rotor in a centrifuge increases from 408 to 1417 rad/s in a time of 5.50 s.
(a) Obtain the angle through which the rotor turns.
rad
(b) What is the magnitude of the angular acceleration?
rad/s2
5- A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration of 0.110 rad/s2. After making 2852 revolutions, its angular speed is 136 rad/s.
(a) What is the initial angular velocity of the turbine?
rad/s
(b) How much time elapses while the turbine is speeding up?
s
part C-
1- The brakes of a truck cause it to slow down by applying a retarding force of 2.50 x 103 N to the truck over a distance of 870 m. What is the magnitude of the work done by this force on the truck?
J
Is the work positive or negative? Why?
2- A cable lifts a 990 kg elevator at a constant velocity for a distance of 30 m. What is the work done by each of the following?
(a) the tension in the cable
J
(b) the elevator's weight
J
3- A person pulls a toboggan for a distance of 30.0 m along the snow with a rope directed 25.0° above the snow. The tension in the rope is 68.0 N.
(a) How much work is done on the toboggan by the tension force?
J
(b) How much work is done if the same tension is directed parallel to the snow?
J
4- During a tug-of-war, team A pulls on team B by applying a force of 1250 N to the rope between them. How much work does team A do if it pulls team B toward them a distance of 1.6 m?
J
5- A person pushes a 16.0 kg shopping cart at a constant velocity for a distance of 20.0 m. She pushes in a direction 30.0° below the horizontal. A 34.0 N frictional force opposes the motion of the cart.
(a) What is the magnitude of the force that the shopper exerts?
N
(b) Determine the work done by the pushing force.
J
(c) Determine the work done by the frictional force.
J
(d) Determine the work done by the gravitational force.
J
6- A 0.064 kg arrow is fired horizontally. The bowstring exerts an average force of 50 N on the arrow over a distance of 0.75 m. With what speed does the arrow leave the bow?
m/s
7- When a 0.045 kg golf ball takes off after being hit, its speed is 40 m/s.
(a) How much work is done on the ball by the club?
J
(b) Assume that the force of the golf club acts parallel to the motion of the ball and that the club is in contact with the ball for a distance of 0.006 m. Ignore the weight of the ball and determine the average force applied to the ball by the club.
N
8- A 6.50 x 104 kg space probe is traveling at a speed of 12000 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe's speed. The retrorockets generate a force of 3.00 105 N over a distance of 2700 km. What is the final speed of the probe?
m/s
9- Relative to the ground, what is the gravitational potential energy of a 55.0 kg person who is at the top of the Sears Tower, a height of 443 m above the ground?
J
10- A 0.60 kg basketball is dropped out of the window that is 5.7 m above the ground. The ball is caught by a person whose hands are 1.1 m above the ground. How much work is done on the ball by its weight?
J
What is the gravitational potential energy of the basketball, relative to the ground when it is released?
J
What is the gravitational potential energy of the basketball when it is caught?
J
How is the change (PEf - PE0) in the ball's gravitational potential energy related to the work done by its weight?