ch 4 FC questions

11. What is the mass on Mercury of an object that weighs 784 N on the earth's surface?

(a) 80 kg The answer follows directly from the fact that weight W is given by W = mg, where m is the mass and g is the acceleration due to the earth's gravity. Thus, m = (784 N)/(9.80 m/s2) = 80.0 kg. The mass is the same on Mercury as on Earth, because mass is an intrinsic property of matter.

5. (4.4) Two forces act on a moving object that has a mass of 27 kg. One force has a magnitude of 12 N and points due south, while the other force has a magnitude of 17 N and points due west. What is the acceleration of the object?

Ans: (c) 0.77 m/s2 directed 35° south of west net force = (-17,-12) Newton's 2nd law gives the answer directly, provided the net force is calculated by vector addition of the two given forces. The direction of the net force gives the direction of the acceleration. net force = mass * acceleration (-17,-12) = 27 * (x-accel ,y-acceler) (x-accel, y-acceleration) = (-17/27 , -12/27) = (-0.629, -0.44) angle of acceleration = Tan^-1 (-0.444.../-0.629629...) = 35.2 degrees below negative (-) x-axis. Magnitude of acceleration = sqrt((-0.629629...)^2 + (-0.444...)^2) = 0.77069 (5dp)

2. Which one of the following descriptions VIOLATES Newton's first law of motion? (a) A small suitcase is at the front of the overhead luggage compartment on an airplane. When the airplane begins its takeoff, the suitcase slides to the rear of the compartment. (b) A glass of water is sitting on a table in the dining car of a train. The train brakes as it nears the station, and the glass slides forward. (c) A rabbit's foot is hanging on a chain from the rearview mirror of a car. As the car accelerates, the rabbit's foot swings toward the windshield. (d) A child is sitting in the back seat of a car and is not wearing a seat belt. The car is traveling forward, and the driver suddenly applies the brakes. The child flies forward against the rear side of the front seat.

(c)Rabbit's Foot. This situation violates the 1st law, which predicts that the rabbit's foot tends to remain in place where it was when the car begins accelerating. The car would leave the rabbit's foot behind. That is, the rabbit's foot would swing away from, not toward, the windshield.

12. (4.8) The apparent weight of a passenger in an elevator is greater than his true weight. Which one of the following is true?

(d) The elevator is either moving upward with an increasing speed or moving downward with a decreasing speed. What matters is the direction of the elevator's acceleration. When the acceleration is upward, the apparent weight is greater than the true weight. When the acceleration is downward, the apparent weight is less than the true weight. In both possibilities the acceleration points upward.

7. (4.5)Which one of the following is true, according to Newton's laws of motion? Ignore friction. (a)A sports utility vehicle (SUV) hits a stationary motorcycle. Since it is stationary, the motorcycle sustains a greater force than the SUV does. (b)A semitrailer truck crashes all the way through a wall. Since the wall collapses, the wall sustains a greater force than the truck does. (c)Sam (18 years old) and his sister (9 years old) go ice skating. They push off against each other and fly apart. Sam flies off with the greater acceleration. (d)Two astronauts on a space walk are throwing a ball back and forth between each other. In this game of catch the distance between them remains constant. (e)None of the above is true, according to the third law.

(e) Answers a and b are false, according to the third law, which states that whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. It does not matter whether one of the bodies is stationary or whether it collapses. Answer c is false, because according to the third law, Sam and his sister experience forces of equal magnitudes during the push-off. Since Sam has the greater mass, he flies off with the smaller acceleration, according to the second law. Answer d is false, because in catching and throwing the ball each astronaut applies a force to it, and, according to the third law, the ball applies an oppositely directed force of equal magnitude to each astronaut. These reaction forces accelerate the astronauts away from each other, so that the distance between them increases.

4. A car has a mass of 1600 kg. It is stuck in the snow and is being pulled out by a cable that applies a force of 7560 N due north. The resistance of the snow and mud also applies a force to the car, which has a magnitude of 7340 N and points due south. What is the acceleration of the car?

0.14 m/s2 north Newton's 2nd law with a net force of 7560 N - 7340 N = 220 N due north gives the answer directly.

9. (4.7) In another solar system a planet has twice the earth's mass and three times the earth's radius. Your weight on this planet is how many times your earth-weight. Assume that the masses of the earth and of the other planet are uniformly distributed.

0.222 Newton's law of gravitation gives the answer directly. According to this law the weight is directly proportional to the mass of the planet, so twice the mass means twice the weight. However, this law also indicates that the weight is inversely proportional to the square of the planet's radius, so three times the radius means one-ninth the weight. Together, these two factors mean that the weight on the planet is 2/9 or 0.222 times your earth-weight.

8. (4.5) Two ice skaters, Paul and Tom, are each holding on to opposite ends of the same rope. Each pulls the other toward him. The magnitude of Paul's acceleration is 1.25 times greater than the magnitude of Tom's acceleration. What is the ratio of Paul's mass to Tom's mass?

0.80 Newton's third law indicates that Paul and Tom apply forces of equal magnitude to each other. According to Newton's second law, the magnitude of each of these forces is the mass times the magnitude of the acceleration. Thus, we have mPaulaPaul = mTomaTom, or mPaul/mTom = aTom/aPaul.

6. A cheetah has an acceleration that has x and y components of ax = 5.3 m/s2 and ay = 3.8 m/s2. The cheetah's mass is 61 kg. Find the net force acting on the cheetah.

4.0 102 N, directed 36° above the x axis Newton's second law gives the answer directly. One method is to determine the total acceleration by vector addition of the two given components. The net force has the same direction as the acceleration.

10.One uniform sphere of matter has a radius of 0.50 m and a mass of 65 kg. A second uniform sphere has a radius of 0.80 m and a mass of 87 kg. The surfaces of the spheres are 1.20 m apart, as measured on a line drawn between the centers of the spheres. What is the magnitude of the gravitational force that each sphere exerts on the other?

6.0 × 10-8 N Newton's law of gravitation gives the answer, provided that the distance between the centers of the spheres is used for r (r = 0.50 m + 1.20 m + 0.80 m), rather than the distance between the surfaces of the spheres.

3. A cup of coffee is sitting on a table in a recreational vehicle (RV). The cup slides toward the rear of the RV. According to Newton's first law, which one or more of the following statements could describe the motion of the RV? (A) The RV is at rest, and the driver suddenly accelerates. (B) The RV is moving forward, and the driver suddenly accelerates. (C) The RV is moving backward, and the driver suddenly hits the brakes.

A, B, & C (ALL) Newton's 1st law states that an object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. All three statements are consistent with the first law.