Two ice skaters are holding hands at the center of a frozen pondwhen an argument ensues. Skater A shoves skater B along ahorizontal direction.
(a) Identify the horizontal forces acting on A.
(b) Identify the horizontal forces acting on B.
(c) Which force is greater, the force on A or the force on B?
(d) Can conservation of momentum be used for the system of A andB?
Defend your answer.
(e) If A has a mass of 0.750 times that of B, and B begins to moveaway with a speed of 2.25 m/s, find the speed of A.

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This experiment involves centripetal force, the force that keeps objects moving in a circular path. This force is perpendicular to the motion and directed towards the center of the circular orbit. By Newton's Second Law when a centripetal force acts on a mass (in a horizontal plane), the force continually changes the direction of the velocity without changing its magnitude, speed. This change in the direction of the velocity accounts for the centripetal acceleration of the mass, whose direction is towards the center. The relationship between the centripetal force, the mass of the orbiting object, and its speed and distance from the center is described by:

EXTENSION QUESTION: When twirling the mass, students found that despite their best efforts, they could not swing the ball so that the cord remained exactly horizontal.

(a) On the diagram of the rotating mass below, draw a force diagram of the forces acting on the mass and identify each force. Do not include any force components in this diagram.

(b) Explain why it is not possible for the ball to swing so that the cord remains exactly horizontal. Write your answer using complete sentence

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1. A physical therapy patient contracts her biceps muscle, andexerts a horizontal force of 180 N on the spring shown in thefigure at right. Assume the forearm rotates at the elbow. a) Drawan extended force diagram of the forearm (everything from the elbowto the tip of the fingers) showing the pivot point and all of theforces acting on the forearm where they actually are applied. Youwonât know the magnitudes (or even the directions) of these forcesuntil you finish the whole problem but just draw reasonable vectorsfor now.
b) Now draw a force diagram with the forearm as a dot. c) Use thefact that the forearm is perfectly stationary at all times to findthe horizontal force that her biceps exerts on her forearm AND theforce exerted by the bone of the upper arm (shown below the biceps)on the forearm (weight = 30N). Note that muscles can only PULL inthe direction along the muscle, but that ligaments (like the onesin the elbow that connect the upper arm with the forearm) can exertforces in any direction. d) Briefly explain in complete Englishsentences (i.e., not just equations) why the bone of the upper armexerts such a large force on the forearm. e) What is the advantageof having the point where the biceps is attached to the forearm soclose to the elbow? What is the disadvantage of having it attachedso close?

2. You are trying to roll your bicycle wheel (of mass m andradius R) over a curb (of height h). To do this, you apply ahorizontal force F in the direction of desired motion. What is theminimum magnitude of the force that will successfully raise thewheel onto the curb when the force is applied (a) at the center ofthe wheel, and (b) at the top of the wheel? (c) In which case isthe magnitude of the force the least?

3. A hay bale is being dragged along a horizontal surface withconstant speed by a force F. The hay bale is 0.6 m high, 0.3m wide,and 0.9 m long (the side the force is applied to, perpendicular tothe direction of motion). The coefficient of kinetic friction is0.33. (a) Find the magnitude of the force, F. (b) Find the height,h, at which the bale will begin to tip over if the force is appliedat that height.

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°

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