Answers Ch.6 30 31 41 Ch.7 15 20 22 33 34 39
30. Below is a diagram of the system before and after the elastic collision:




Solve for the final velocity of each block.
31. Below is a diagram of the system before and after the elastic collision:




Solve for the final velocity of each block.
41. Below is a diagram of the system before and after the elastic collision:



(a) Solve for the final velocity of each block. Note that you get the speed by taking the absolute value of the velocity component

(b) Repeat the calculation of part (a) assuming m2 = 10 g.
(c) Find the two possible final kinetic energy of m1, which is given by:

Use the velocities you found for m1 in part (a) and part (b).
15. (a)

(b)

(c ) Use the relationship between the linear velocity, the radius and the angular velocity.

Remember to convert rev to rads!

20. (a)

But,

Find v.

(b)

The angular acceleration is found in part (a). Note that the car starts from rest. Note also that you can get the second angular velocity using the relationship that :

(c )

Find the change in time. Remember that the car starts from rest!

22 .In this case the force causing circular motion is the force of static friction of the ground on the tires. See example 7.6. In this problem, however, you solve for v.

33.

Compute the magnitude and the angle.

34. You will have to solve a quadratic equation! But don't panic. It's easy once you set things up. At the point at which the net force on the object is zero, we have the following picture:

At the point indicated above, the force magnitude F2 due to the earth equals the force magnitude F1 due to the sun. Thus:

Note that G and the mass m of the object cancels on both sides of the equation. d = distance between the sun and the earth. x = distance of object from the sun. After cross-multiplying and simplifying, we get:

Solve for the value of x that references a point that is between the sun and the earth. You will have two mathematical possibilities. Choose the value of x that makes sense physically. After all, the science of physics uses mathematics only as a tool , not a magic wand. You must think physically and draw from mathematics selectively in order to explain the world accurately!

39. (a) Use equation 7.19. However, you must be careful! The problem gives you the height above the surface of the earth. Eqn. 7.19 references the distance from the center of the earth. Thus you must find that distance by using the radius of the earth!
(b) Use eqn. 7.17. However, you must be careful for the same reason given in part (a)!