## 23 Sep An astronaut takes her bathroom scales to the moon, where g = 1.6 m/s2. On the moon, compared to at home on earth:

Question 1An astronaut takes her bathroom scales to the moon, where g = 1.6 m/s2. On the moon, compared to at home on earth:

Her weight is less, and her mass is the same.

Her weight is less, and her mass is less.

Her weight is zero, and her mass is the same.

Her weight is the same, and her mass is the same

Her weight is the same, and her mass is less.

Question 2A ring, seen from above, is pulled on by three forces. The ring is not moving. How big is the force F?

Question 3The cart is initially at rest. Force is applied to the cart for time Δt, after which the car has speed v. Suppose the same force is applied for the same time to a second cart with twice the mass. Friction is negligible. Afterward, the second cart’s speed will be

2 v

4 v

0.5 v

v

0.25 v

Question 4 The force of friction is described by

the law of friction.

the theory of friction.

a model of friction.

the friction hypothesis.

Question 5 A box is being pulled to the right over a rough surface. T >fk , so the box is speeding up. Suddenly the rope breaks. What happens? The box

Slows steadily until it stops.

Stops immediately.

Keeps its speed for a short while, then slows and stops.

Continues speeding up for a short while, then slows and stops.

Continues with the speed it had when the rope broke.

PROBLEM-SOLVING STRATEGY 6.1 Newtonian mechanics

MODEL: Make simplifying assumptions.

VISUALIZE: Draw a pictorial representation.

• Show important points in the motion with a sketch, establish a coordinate system, define symbols, and identify what the problem is trying you to find. This is the process of translating words into symbols.

• Use a motion diagram to determine the object’s acceleration vector

• Identify all forces acting on the object, and show them on a free-body diagram.

• It’s OK to go back and forth between these steps as you visualize the situation.

SOLVE: The mathematical representation is based on Newton’s second law:

The vector sum of the forces is found directly from the free-body diagram. Depending on the problem, either

• Solve for the acceleration, and then use kinematics to find velocities and positions; or

• Use kinematics to determine the acceleration, and then solve for unknown forces.

ASSESS: Check that your result has the correct units, is reasonable, and answers the question.

Question 6Part 1 This question has multiple parts.

A box of mass 3.0 kg slides down a rough vertical wall. The gravitational force on the box is 29.4 N . When the box reaches a speed of 2.5 m/s , you start pushing on one edge of the box at a 45 degrees angle (use degrees in your calculations throughout this problem) with a constant force of magnitude Fp = 23.0 N , as shown in the figure . There is now a frictional force between the box and the wall of magnitude 13.0 N . How fast is the box sliding 2.8 s after you started pushing on it?

Model

Start by making a simplifying assumption: We will assume all the forces acting on the box are constant, so now you can model the box as a particle moving with a constant acceleration.

Visualize

Using our simplified model, in which we know that the forces are constant (but assume for now that we don’t know what their magnitudes are), which, perhaps more than one, of the following motion diagrams could be a reasonable representation of the motion of the box? Check all that apply.

Correct Answer

A

B

C

D

Question 7Still using our simplified model (in which we do not know the magnitudes of the forces), draw a free-body diagram showing all the forces acting on the box after you start pushing on it. The positive y axis is taken to be upward. The black dot represents the box. Since our model is about having constant forces of unknown magnitude, the vectors are not to scale.

Which of the following free body diagram is correct?

Question 8Part 3.

Find the box’s speed vf at 2.8 s after you first started pushing on it. Express you answer in m/s

—-Hint 1. How to approach the problem

This is a one-dimensional kinematics problem. You are given the box’s initial speed and need to calculate its final speed after a certain period of time. You know that motion occurs only in the vertical direction, so there’s no need to write down any equation in the x direction. All you need is ay, the y component of the box’s acceleration, which can be calculated by applying Newton’s second law in the y direction.

Hint 2. Set up Newton’s second law in the y direction

Newton’s second law states that (Fnet)y, the y component of the net force acting on an object, is equal to the y component of the object’s acceleration multiplied by its mass, that is, (Fnet)y=may. Using the coordinate system show in questions above, enter an expression for (Fnet)y in terms of the forces acting on the box.

For the push force FP, you will need only the y component.

Hint 3. Once you know ay, use constant acceleration kinematics to find vfy

2.6 (with margin: 0.2)

Question 9Assuming that the angle at which you push on the edge of the box is again 45 degrees, with what magnitude of force Fp should you push if the box were to slide down the wall at a constant velocity? Express your answer in Newton.

Note that, in general, the magnitude of the friction force will change if you change the magnitude of the pushing force. Thus, for this part, assume that the magnitude of the friction force is fk=0.516Fp.

Hint 1. Dynamic equilibrium

If the box slides down the wall at a constant velocity, its acceleration must be zero. This is the condition for dynamical equilibrium, or . Set up again Newton’s second law in the y direction as you did in the previous part, keeping in mind that now the magnitude Fp of the pushing force is unknown. Use the equilibrium condition (Fnet)y=0, and solve for Fp.

Question 10A loudspeaker of mass 23.0 kg is suspended a distance of h = 1.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 2.50 m.

What is the tension T in each of the cables? Write your answer in N.

Hint 1. How to approach the problem

We know that and , the tension forces, are directed along their respective cables. Since the loudspeaker is in equilibrium, the vector sum of and must exactly balance any other forces that act on the loudspeaker. Since the two cables are at equal angles, there is no reason for the magnitudes of the tensions in the cables to differ. The tensions in the two cables are in fact the same. Therefore, both of them can be called T. Then, using T1y=T2y=Tsinθ, where θ is the angle between a cable and the ceiling, solve for the value of T.

Hint 2. The two tensions force must cancel the force of gravity in the y direction since the loudspeaker is not accelerating.

Question 11Given the mass of a bucket and its upward acceleration, find the applied force

In this question you can approximate g = 10 m/s2

Hint 1. How to approach the problem

Apply Newton’s second law to the bucket, ΣFy=may, making sure to include all the forces acting on it. The tension force will be on the left hand side. Make sure to include the acceleration when you solve for the tension

Hint 2: Be careful with the signs.

The force of gravity is downward and the ay also has a sign.

A 6-kg bucket of water is being pulled straight up by a string at a constant speed. What is the tension in the rope?

The bucket has an upward constant acceleration of magnitude 3 m/s^2. What is the tension in the rope?

The bucket has a downward acceleration, with a constant acceleration of magnitude 3 m/s^2. What is the tension in the rope?

Other Incorrect Match Options:

• It is decreasing as the speed increases.

• 0 N because the bucket has no acceleration.

• It is increasing as the speed increases.

Question 12A chair of weight 135 N lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of F = 39.0 N directed at an angle of 39.0 degree below the horizontal and the chair slides along the floor.

Using Newton’s laws, calculate n, the magnitude of the normal force that the floor exerts on the chair. Express your answer in Newton.

Question 13During an experiment, a crate is pulled along a rough horizontal surface by a force and the magnitude of the acceleration along the x direction, ax, is measured.(Figure 1) The vector has a component along the x direction of magnitude Fx. The experiment is repeated several times, with different values of Fx each time, while maintaining a constant value for, Fy, the vertical component of .

Part 1

Create a plot of the force of static friction, fs, versus the x component of the pulling force, Fx, for the experiment. Let the point Fmin, along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fs, Fx, and Fmin.

Hint 1:

There are two important characteristics to keep in mind about the the force of static friction:

• Only a stationary object can be acted upon by the force of static friction.

• fs≤μsn, where μs is the coefficient of static friction and n is the magnitude of the normal force. This inequality means that the actual force of static friction can have any magnitude between zero and a maximum value of μsn.

A

B

C

D

E

Question 14Create a plot of the force of kinetic friction, fk, versus the x component of the pulling force, Fx, for the experiment. Let the point Fmin, along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fk, Fx, and Fmin.

There are three important characteristics to keep in mind about the force of kinetic friction:

• Only an object that is sliding with respect to a surface can be acted upon by the force of kinetic friction.

• points in a direction that is parallel to the surface of contact and opposes the motion of the object.

• fk=μkn, where μk is the coefficient of kinetic friction and N is the magnitude of the normal force.

A

B

C

D

Question 15After all the trials are completed, a graph of acceleration ax as a function of force Fx is plotted. Assuming the presence of both static and kinetic friction, which of the following graphs is most nearly correct?

A

B

C

D

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