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Newton's Second Law Problems:

In all problems start with a complete free body diagram. Indicate and Newton's Third Law pairs on your diagrams.

1. Boxes A and B, with masses m_A and m_B can move on a horizontal frictionless surface. You push horizontally with a push P on block A. (a) Find the acceleration of the boxes. (b) Find the force between the boxes. Answers may contain symbols already given plus any constants like g.(c) Suppose m_A = 10 kg and m_B = 40 kg, and P = 100 N. What are the numerical answers? (d) Suppose m_A = 40 kg and m_B = 10 kg, and P = 100 N. What are the numerical answers?

2. A book of mass m is pushed against a smooth frictionless wall by a force P that makes an angle q with the vertical. Find (a) the normal force on the book and (b) its acceleration in terms of P, m, q, and constants. (c) Look at limiting cases (large and small angles) to see if it makes sense.

3. You are skiing on a hill inclined at q to the horizontal where there is a constant frictional force f. Find the normal force and your acceleration in terms of your mass, m, f, q, and constants. Look at limiting cases to see if the answer makes sense.

4. A Ferris Wheel has a radius of 11.0 m and rotates once every 11.0 s. What is the force of the chair seat on you at each of the three positions, top, side, and bottom? Answer as a multiple of your weight (e.g. 1.4 mg).

5. You whirl a ball of mass 0.40 kg on a string of length 0.90 m. At the point shown the angle of the string from the vertical is 30° and the ball has a speed of 3.50 m/s.

(a) Find the tension in the string.

(b) What is the acceleration of the ball, tangential and radial components?

(c) Now consider the ball at the top of the circle. What is the smallest speed of the ball so that the ball continues in a circle?

6. I have a horizontal table that is very low friction. On it I place a pair of blocks, with m₁ on top of m₂. Between the blocks there is friction, with static coefficient m_s and kinetic coefficient m_k I attach a rope to the lower block and pull with a pull P acting at an angle q above the horizontal. If the pull is small the two blocks move together. If the pull is large they move relative to each other.

(a) For a large pull, find the acceleration of each block.

(b) For a small pull, find the common acceleration, and find the actual force of friction.

Try using m₁ = 0.600 kg, m₂ = 2.400 kg, q = 30.0°, m_s = 0.450, m_k = 0.350 and for a small pull, P = 5.000 N, large pull P = 20.000 N. What answers do you get? Do they make sense?

7. You are pushing a box uphill the hill has a pitch of 15° above the horizontal, and the static and kinetic friction coefficients between the box and the hill are 0.45 and 0.35. The box has a mass of 40 kg. You push horizontally with a push of 180 N, and the box is initially moving uphill. Find the acceleration of the box.

8. While visiting a friend in San Francisco you decide to drive around the city. You turn a corner and are driving up a steep hill. Suddenly, a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop leaving a 50 foot long skid mark on the street. The boy calmly walks away but a policeman watching from the sidewalk walks over and gives you a ticket for speeding. You are still shaking from the experience when he points out that the speed limit on this street is 25 mph. After you recover your wits, you examine the situation more closely. You determine that the street makes an angle of 20o with the horizontal and that the coefficient of static friction between your tires and the street is 0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car's information book tells you that the mass of your car is 1570 kg. You weigh 130 lbs. Witnesses say that the boy had a weight of about 60 lbs. and took 3.0 seconds to cross the 15 foot wide street. Will you fight the ticket in court?