Physics 1028A/B Lecture Notes - Lecture 9: Massachusetts Route 2, Resultant Force

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16 Oct 2018

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Dynamics: the study of forces and their effects on the motion of objects. Normal force: the force perpendicular to surfaces in contact with each other. Force of friction: the force parallel to surfaces in contact with each other, due to forces between molecules in the surfaces. Static friction: the friction force exerted between surfaces that are not moving relative to each other. Kinetic friction: the friction force exerted between surfaces moving relative to each other. Tension: a force exerted on objects - acting away from the object being considered - by pulling it. Contact forces: forces that, in order to be exerted, require contact between objects e. g. friction, normal and tension. Action-at-a-distance forces: forces that do not require contact between objects in order to be exerted e. g. gravity, electrostatic and magnetic. Free-body diagram (fbd): a diagram in which only the forces acting on a particular object are shown.

Related Questions

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let F_u and F_d (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless so that its weight is negligible compared with the tension. (This is not a ridiculous approximation-modern rope material such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

At point 1, a downward force of magnitude F_ad acts on section a.
At point 1, an upward force of magnitude F_bu acts on section b.
At point 1, the tension in the rope is T₁.
At point 2, a downward force of magnitude F_bd acts on section b.
At point 2, an upward force of magnitude F_cu acts on section c.
At point 2, the tension in the rope is T₂.

(A) What is the magnitude F_ad of the downward force on section a?

(B) What is the magnitude F_bu of the upward force on section b?

(C) The magnitude of the upward force on c, F_cu, and the magnitude of the downward force on b, F_bd, are equal because of which of Newton's laws?

(D) The magnitude of the force F_bu is ______ F_bd.

(E) Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

(a) F_u > F_d

(b) F_u = F_d

(F) The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true?

(a) The tension in the rope is everywhere the same.

(b) The magnitudes of the forces exerted on the two objects by the rope are the same.

(d) The forces exerted on the two objects by the rope must be in the direction of the rope.

ambergiraffe181

1.A 4.00-kg block rests between the floor and a3.00-kg block asshown in the Figure. The 3.00-kg block is tied toa wall by ahorizontal rope. If the coefficient of static frictionis 0.800between each pair of surfaces in contact:

a) Draw free-body diagrams for the two boxesidentifying all ofthe forces acting on each of themasses.

b) Calculate the minimum force F that mustbe appliedhorizontally to the 4.00- kg block to make itmove?

c) What will be the tension in the rope underthe condition in(b).

2.Two skaters, a man and a woman,are standing on ice. Neglectany friction between the skate bladesand the ice. The woman pusheson the man with a certain force thatis parallel to the ground.

a) Must the man accelerate underthe action of this force? If so,what three factors determine themagnitude and direction of hisacceleration?

b) Is there a corresponding forceexerted on the woman? If so,where does itoriginate?

c) Is this force on the womanrelated to the magnitude anddirection of the force the womanexerts on the man? If so, how?

d) The mass of the man is 74 kgand that of the woman is 50 kg.The woman pushes on the man with aforce of 45 N due east. Determinethe acceleration (magnitude anddirection) of (i) the man and (ii)the woman

1.

While helping a friend move, you push a 11.5 kg dolly with a forceof 11.0 N. Assume there are no other forces acting on the dolly. Ifthe dolly starts at rest, how far does it move in 3.50 s?
1 m

2.

At a lumberjack competition an axe with a mass of 1.25 kg is thrownat a target with a speed of 41 m/s. When it hits the target, itpenetrates to a depth of 0.055 m.
(a) What was the average force exerted by the target on theaxe?
1 N

(b) If the mass of the axe is halved, and the force exerted by thetarget on the axe remains the same, by what multiplicative factordoes the penetration depth change?
2
It doubles. It increases by a factor of the square root of two. Itdoes not change. It decreases by a factor of the square root oftwo. It halves.
Your work in question(s) will also be submitted or saved.
3

Your 1500 kg car pulls a 540 kg trailer away from a stop sign withan acceleration of 2.00 m/s2. (Note the answers should be given inkN.)
(a) What is the net force exerted by the car on the trailer?
1 kN

(b) What force does the trailer exert on the car?
2 kN

(c) What is the net force acting on the car?
3 kN

4.

Two boxes sit next to, and touching, each other on a frictionlesshorizontal surface. The lighter box has a mass of 5.31 kg and theheavier box has a mass of 7.29 kg.
(a) Find the contact force between these boxes when a horizontalforce of 6.1 N is applied to the light one.
1 N

(b) If the 6.1 N force is applied to the heavy box instead, is thecontact force between the boxes the same as, greater than, or lessthan the contact force in part (a)?
2

(c) Verify your answer to part (b) by calculating the contact forcein this case.
3 N

5.

A child sits in a wagon and together they have a mass of 25 kg. Thewagon is pulled with a constant speed by a handle that is at anangle of 22Â° above the horizontal. If the normal force exerted onthe wagon is 210 N, what is the force F applied to thehandle?
1 N

6.

An object acted on by three forces moves with constant velocity.One force acting on the object is in the positive x direction andhas a magnitude of 6.7 N; a second force has a magnitude of 4.5 Nand points in the negative y direction. Find the direction andmagnitude of the third force acting on the object.
1 N
2Â° (counterclockwise from the +x axis)

7.

A chain is used to lift a 1200 kg car vertically upward with anacceleration of 0.90 m/s2. What is the tension in the chain?
1 N

8.

A 22.5 kg box (m1) rests on a table.

(a) What is the weight of the box?
1 N
What is the normal force acting on it?
2 N (upward)
(b) A 12.5 kg box (m2) is placed directly on top of the 22.5 kgbox.
Determine the normal force that the table exerts on the 22.5 kgbox.
3 N (upward)
Determine the normal force that the 22.5 kg box exerts on the 12.5kg box.
4 N (upward)

9.

Your friend has a weight of 127 lb when standing on a scale. Youtake the scale to an elevator where you notice your friend's weighton the scale reads 108 lb. What are the direction and magnitude ofthe elevator's acceleration?
Direction 1
Magnitude 2 m/s2

10.

When you lift a package with a force of 82 N, the packageaccelerates upward at a rate of a. If, instead, you lift with aforce of 93 N, the package now has an acceleration of 8 multipliedby a.
(a) Find the weight of the package.
1 N

(b) Find the acceleration a.
2 m/s2

11.

One 3.1 kg paint bucket is hanging by a massless cord from another3.1 kg paint bucket, also hanging by a massless cord, as shownbelow.

(a) If the buckets are at rest, what is the tension in eachcord?
(lower cord) 1 N
(upper cord) 2 N

(b) If the two buckets are pulled upward with an acceleration of1.30 m/s2 by the upper cord, calculate the tension in eachcord.
(lower cord) 3 N
(upper cord)5

12)
Your friend has a pair of fuzzy dice with a mass of 1.32 g hangingfrom his rear-view mirror.
(a) When he accelerates from a stoplight, the dice deflect backwardtoward the rear of the car hanging at an angle of 6.18Â° relative tothe vertical. Find the tension in the string holding thedice.
N

(b) At what angle to the vertical will the tension in the string betwice the weight of the dice?
Â°

Physics 1028A/B Lecture Notes - Lecture 9: Massachusetts Route 2, Resultant Force

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