Problem 112

Two Skaters Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The woman pushes on the man with a certain force that is parallel to the ground. (a) Must the man accelerate under the action of this force? If so, what three factors determine the magnitude and direction of his acceleration in the horizontal direction? No, because the force exerted on the man could be balanced by his weight. No, because the force exerted on the man could be balanced by the normal force exerted by the ice that opposes this force. Yes. The three factors are (1) the magnitude and (2) the direction of the force she exerts on him and (3) his mass. Yes. The three factors are (1) the magnitude and (2) the direction of the force she exerts on him and (3) his weight. Yes. The three factors are (1) the magnitude and (2) the direction of the force she exerts on him and (3) the normal force exerted on him by the ice. Correct. There is only one force acting on the man in the horizontal direction, so it is the net force and he must accelerate in this direction. Newton's second law (Equation 4.1) states that the acceleration depends on the magnitude and direction of the net force acting on the man, divided by his mass. (b) Is there a corresponding force exerted on the woman? If so, how is this force related to the magnitude and direction of the force that she exerts on the man? Yes, the man exerts a force on the woman. This force has the same magnitude, but an opposite direction compared to that of the force that the woman exerts on the man. There is no corresponding force exerted on the woman. Yes, the man exerts a force on the woman, but this force is smaller in magnitude than the force that the woman exerts on the man. Yes, the man exerts a force on the woman, but this force is greater in magnitude than the force that the woman exerts on the man. Correct. Newton's third law, the action-reaction law, states that if the woman exerts a force on the man, the man also simultaneously exerts a force on the woman. The two action reaction forces have the same magnitude, but opposite directions.

The mass of the man is 89 kg and that of the woman is 65 kg. The woman pushes on the man with a force of 58 N, due east. (c) What is the algebraic expression for the magnitude am of the man's acceleration? Express your answer in terms of the magnitude Fm of the force exerted on the man and his mass mm. (Answer using F_m for Fm and m_m for mm.) am = Enter a mathematical expression. 3 (d) What are the magnitude and direction of the man's acceleration? Number Unit Direction Enter a number. 4 5 ---Select--- kg N kg·m kg·N m/s m/s^2 6 ---Select--- due north due east due south due west (e) What is the algebraic expression for the magnitude awoman of the woman's acceleration? Express your answer in terms of the magnitude Fw of the force exerted on the woman and her mass mw. (Answer using F_w for Fw and m_w for mw.) aw = Enter a mathematical expression. 7 (f) What are the magnitude and direction of the woman's acceleration? Number Unit Direction Enter a number. 8 9 ---Select--- kg N kg·m kg·N m/s m/s^2 10 ---Select--- due north due east due south due west

Problem 113

Pushing Refrigerators A person is attempting to push a refrigerator across a room. He exerts a horizontal force on the refrigerator, but it does not move. (a) What other horizontal force must be acting on the refrigerator? 1 The reaction force that arises because of the pushing force. The normal force exerted by the floor.     The kinetic frictional force. The gravitational force. The static frictional force. Correct! The static frictional force is a horizontal force, and it is exerted on the refrigerator by the floor. (b) How are the magnitude and direction of this other horizontal force related to the force that the person exerts? The magnitude is the same as that of the force exerted by the person, but the direction is opposite to that of the force exerted by the person. The magnitude is different than that of the force exerted by the person, but the direction is the same as that of the force exerted by the person. The magnitude is the same as that of the force exerted by the person, and the direction is also the same as that of the force exerted by the person. The magnitude is different than that of the force exerted by the person, and the direction is opposite to that of the force exerted by the person. Correct! The refrigerator does not move, so its acceleration is zero. According to Newtons second law, the net force acting on the refrigerator must also be zero. The two forces acting on the refrigerator will add together to produce a net force of zero only if they have the same magnitudes and opposite directions. (c) Suppose that the person applies the force such that it is the largest possible force before the refrigerator begins to move. What factor(s) determine the magnitude of this force? 3 The coefficient of static friction μs and the magnitude FN of the normal force. Only the magnitude FN of the normal force.     The coefficient of kinetic friction μk and the magnitude FN of the normal force. Only the coefficient of kinetic friction μk. Only the coefficient of static friction μs. Correct! Just before the refrigerator begins to move, it is in equilibrium, with the pushing force and the static frictional force having equal magnitudes. Both the coefficient of static friction and the magnitude of the normal force determine the magnitude of the static frictional force and, hence, the pushing force. See Section 4.9 for the complete picture.

A person pushes on a 60 kg refrigerator with a horizontal force of -263 N; the minus sign indicates that the force is directed along the -x direction. The coefficient of static friction is 0.73. (d) If the refrigerator does not move, what is the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? Specify the direction by including in your answer an explicit algebraic sign along with the magnitude. +/- Amount Unit 4 ---Select--- - + Enter a number. 5 6 ---Select--- N kg·N kg kg·m (e) What is the algebraic expression for the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move? Express your answer in terms of the coefficient of static friction μs, the mass m of the refrigerator, and the magnitude g of the acceleration due to gravity. (Answer using mu_s, m, and g as needed.) Magnitude of Force = Enter a mathematical expression. 7 (f) What is the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move? Enter a number. 8 9 ---Select--- kg·m kg·N N kg

Only two forces act on an object (mass = 4.30 kg), as in the drawing. (F = 66.0 N.) Find the magnitude and direction (relative to the x axis) of the acceleration of the object.

Enter a number.

1 m/s²

Enter a number.

2° (counterclockwise from the +x axis)

A 83.0 kg person stands on a scale in an elevator. What is the apparent weight in each of the following situations?

(a) when the elevator is accelerating upward with an acceleration of 2.00 m/s²

Enter a number.

1 N
Your answer differs from the correct answer by 10% to 100%.
(b) when the elevator is moving upward at a constant speed

Enter a number.

2 N

(c) when the elevator is accelerating downward with an acceleration of 1.00 m/s²

Enter a number.

3 N

As part a of the drawing shows, two blocks are connected by a rope that passes over a set of pulleys. One block has a weight of m₁ = 512 N, and the other has a weight of m₂ = 908 N. The rope and the pulleys are massless and there is no friction.

Two horizontal forces, F₁ and F₂, are acting on a box, but only F₁ is shown (see the drawing).

F₂ can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. What is the direction of F₂ and how does its magnitude compare to the magnitude of F₁ when the following is true?

(a) The acceleration of the box is positive.
F₂ 1 ---Select--- must be to the right must be to the left can be either to the right or the left and its magnitude is 2 ---Select--- greater than less than equal to not enough information to decide F₁.
(b) The acceleration of the box is negative.
F₂ 3 ---Select--- must be to the right must be to the left can be either to the right or the left and its magnitude is 4 ---Select--- greater than less than equal to not enough information to decide F₁.
(c) The acceleration of the box is zero.
F₂ 5 ---Select--- must be to the right must be to the left can be either to the right or the left and its magnitude is 6 ---Select--- greater than less than equal to not enough information to decide F₁.

Suppose that F₁ = 10.7 N and the mass of the box is 2.5 kg. Find the magnitude and direction of F₂ when the following is true (use the sign of your answers to indicate direction). Be sure that your answers are consistent with your answers to the Concept Questions.

(d) The acceleration of the box is +5.0 m/s².

Enter a number.

7 N

(e) The acceleration of the box is -5.0 m/s².

Enter a number.

8 N

(f) The acceleration of the box is zero.

Enter a number.

9 N

Mass on a Spring

After running the simulation press the Reset button to activate the sliders. To get the total energy graph to display correctly after changing the initial velocity, hit the Reset button again.

First experiment with the simulation to see what effect changing the initial velocity and the mass has on the motion. Then consider the following four cases, which differ in the settings used in the simulation above:

Case A: Initial velocity = +v; Mass = m
Case B: Initial velocity = -v; Mass = m
Case C: Initial velocity = 0; Mass = m
Case D: Initial velocity = +2v; Mass = m

Predict the results of the questions below, and then use the simulation to verify your predictions.

(a) Rank these cases based on the oscillation amplitude, from largest to smallest (use the notation > or =, for example A>B=D>C).

1

(b) Rank these cases based on the time (after t=0) the mass first passes through the equilibrium position, from longest time to shortest time (use the notation > or =, for example A>B=D>C).

2

Collisions in One Dimension

In the simulation above Ball 1 has a mass M and Ball 2 has a mass nM, where n is an integer. Ball 1 has an initial velocity of v and ball 2 has an initial velocity of -v. Two collisions are carried out with these same initial conditions.

First, the balls undergo a completely inelastic collision (elasticity = 0) where the velocity of both balls after the collision is -0.500 v.

(a) What is the value of n, the ratio of the mass of ball 2 to the mass of ball 1?

1

The same initial conditions are set up but this time the collision is elastic (elasticity = 1). The total kinetic energy both before and after the collision is 384.00 J and the total momentum both before and after the collision is -48.00 kg m/s.

(b) What is M, the mass of ball 1?

2 kg

(c) What is v, the speed of ball 1 before the collision?

3 m/s

AC Circuit with only One Circuit Element

(a) Given the limits on the sliders available to you in the simulation, what are the maximum and minimum values of the "Maximum current" that can be obtained in the simulation?

The maximum possible "Maximum current" is

Enter a number.

1 A.

The minimum possible "Maximum current" is

Enter a number.

2 A.

(b) Which of the following will always result in increasing the "Maximum current" value in an AC Circuit with only one circuit element? Select all that apply.

(c) You have either a resistor, a capacitor, or an inductor connected to an AC source. As you increase the frequency of the voltage you notice that the maximum current increases linearly with frequency. What, if anything, can you conclude about what you have connected to your AC source?