Ch 6 Homework Name: Homework problems are from the Serway & Vuille 10 th edition. Follow the instructions and show your work clearly. 1. (Conceptual questions 6.) A skater is standing still on a frictionless ice rink. Her friend throws a Frisbee straight to her. In which of the following cases is the largest momentum transferred to the skater? (a) The skater catches the Frisbee and holds onto it (b) The skater catches the Frisbee, holds it momentarily, and throws it back to her friend. Explain your answer. 2.(Problem 1) Calculate the magnitude of the linear momentum for the following cases (a) A proton with mass equal to Kg, moving with a speed of m/s.
(b) A 15.0-kg bullet moving with a speed of 10.0 m/s. (c) A 75.0-kg printer running with a speed of 10.0 m/s. (d) The earth(mass = kg) moving with an orbital speed equal to m/s. 3. (Problem 15) The force shown in the force versus time diagram in the figure below acts on a 1.5-kg object.
(a) Find the impulse of the force.(hint: The area under the curve is the impulse) (b) Find the final velocity of the object if it is initially at rest (c) Find the Final velocity of the object if it is initially moving along the x-axis with a velocity of -2.0 m/s
4. (Problem 18) A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of θ=60.0 with the plain of the wall. It bounces off the wall with the same speed and angle (See the Figure below). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball? (a) Define a coordinate system on the figure above and label all physical quantities in this problem using letters you choose. (b) Calculate the difference between initial and final momentum of the ball in the x- and y- directions. X-direction Y-direction Variable value(kg m/s) variable value(kg m/s) x-component of Initial momentum: x-component of Initial momentum: x-component of Final momentum : x-component of Final momentum: p x p y (c) Find the average force exerted by the wall on the ball.
5. (Problem 21) High-speed stroboscopic photographs show that the head of a 200-g golf club is traveling at 55 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40 m/s. Find the speed of the golf ball just after impact. (a) Draw a diagram and label all physical quantities using variables you choose. (b) Calculate the initial momentum of the club and the ball (c) Find the speed of the golf ball just after the impact.
6. (Problem 25) An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she s on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it. (a) Draw a diagram and label all physical quantities in this problem using letters you choose. (b) Find the speed of the astronaut after she throws the oxygen tank in terms of the variable you choose above. (c) Using numbers above, calculate the speed of the astronaut.
(d) Determine the maximum distance she can be from the craft and still return within 2.00 min(amount of time the air in her helmet remains breathable) (e) Explain in terms of Newton s law of motion why this strategy works. 7. (Problem 32) A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4500 N. If the impact time is 0.100 s, does a bone break? (a) Draw a diagram.
(b) Calculate the initial momentum of the ice skater moving at 10.0 m/s. (c) Calculate the change of the momentum of each skater. (d) If the impact time is 0.100 s, does a bone break?
8. (Problem 38) Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s as in Figure (a) below. After the collision, the orange disk moves in a direction that makes an angle of 37.0 with the horizontal axis while the green disk makes angle of 53.0 with this axis as in Figure (b) below. Determine the speed of each disk after the collision. (a) Define coordinate system on the figure above and define variables.
(b) Write x- and y- components of initial and final momentum in terms of variable you define. Variable Initial X-direction Values in terms of variables you define variable Initial Y-direction Values in terms of variables you define Final Final (c) Write the initial and final kinetic energy in terms of the variables you define. Initial Kinetic Energy Final Kinetic Energy (d) Determine the speed of each disk after the collision.
9. (Problem 40) A bullet of mass m =8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a table of height h = 1.00 m. (See the figure below.) The bullet remains in the block, and after the impact the block lands d = 2.00m from the bottom of the table. Determine the initial speed of the bullet. (a) Define a coordinate system and label all physical quantities using letters you choose. (b) Find the speed of the block and the bullet after the bullet hits the block in terms of the variable defined the problem and variables you define.
(c) Find the time to reach the ground in terms of the variables defined. (Hint: the block is free falling) (d) Find the distance d from the bottom of the table in terms of the variable defined. (e) Solve the answer from the part d for the initial speed of the bullet and find the initial velocity of the bullet.
10. (Problem 57) Two objects of masses m 1 = 0.56 kg and m 2 = 0.88 kg are placed on a horizontal frictionless surface and a compressing spring of force constant k = 280 N/m is placed between them as in Figure (a) below. Neglect the mass of the spring. The spring is not attached to either objects and is compressed a distance of 9.8 cm. If the objects are released from rest, find the final velocity of each object as shown in Figure (b) (a) Define a coordinate system. (b) Write down the initial and final total energy. Initial Energy Final Energy
(c) Find the final velocity of each object using the law of momentum conservation.