Supplementary Problems 2 - Forces

Follow these general steps to solve the problems below.
1. Draw a picture.
2. Draw and label all the forces acting on the object.
3. Install an appropriate coordinate system.
4. Resolve any vectors that are not parallel to the axes.
5. Apply Newton's Second Law.


F-1 A box weighing 20 N rests on a horizontal surface. The coefficient of static friction is .4; the coefficient of sliding friction is .2.
a) How large is the friction force exerted on the box as it rests on the table?
b) How great will the friction force be a horizontal force of 5 N is exerted on the box?
c) What is the minimum force that will start the box in motion?
d) What is the minimum force necessary to keep the box in motion once it has started?
e) If the applied force is 10 N, how great is the friction force?

Extended solution

F-2 A hockey puck leaves a player’s stick with a velocity of 10 m/s and slides 40 m before coming to rest. Find the coefficient of friction between the puck and the ice. Extended solution
[Mikey’s note: Like so many other problems in this set, this problem is made more difficult for the student because several intervening questions need to be answered before addressing the question at hand. Take a moment and list the steps that need to be taken to answer the question.]

F-3 A large box (M = 50 kg) rests on a horizontal surface where u = .6. What minimum force is necessary to cause the box to move a) by attaching a rope which is pulled horizontally to the right? b) by attaching a rope that is pulled 30 degrees above the horizontal? c) by pushing down and to the right 20 degrees below horizontal

F4. A 1000 N block is supported at a common point on the block by two cables. Cable A, attached to the left side, makes an angle of 50 degrees with the vertical. Cable B on the right makes an anagle of 30 degrees with the vertical. Find the tension on each cable.

F-5 . A crane is used to lift a heavy load. (Ask for a drawing.) Determine the tension (T) on the cable and the compression (C) of the boom. Assume mass of load is 103 kg.

F-6 A woman who weighs 540N (about 120 lbs) steps into an elevator car and immediately stands on the ever-present bathroom scale. What does the scale read if a) the car is at rest? b) the car is accelerating upward at 3 m/s^2? c) if the car is moving upward with a constant speed of 3 m/s. d) if the car is acceleration downward at 3 m/s^2. (Hint: before beginning this problem, determine exactly what a bathroom scale measures.)

F-7 An inclined plane is tilted 37o above the horizontal. The coefficient of friction between th plane and a block sliding on it is .4. If the block is projected up the plane with a speed of 12 m/s, a) how far up the plane does it go? b) What is the elapsd time before stopping? c) Does it slide down again? How do you know? d) If it does slide down, how does the travel time up compare with the travel time down? e) What change(s) would you make to ensure that the block did not slide down? Show the mathematical impact of your changes on the numbers.

F-8 See figure 8. A window washer pushes his scrub brush up a vertical window by applying a force F on the window. The brush handle makes an angle of 37o with the vertical. The brush weighs 6 N and the coefficient of kinetic friction is .4. Calculate a)the magnitude of F; and b) the normal force exerted by the window on the brush.

F-10 A crate rests on the back of a truck where the coefficient of friction is .4. The truck is initially at rest but accelerates to some speed. What is the largest acceleration that the truck can have without causing the crate to slip?

F-10 A block (m = 10 kg) is dragged across the floor by a force of 100 N applied through an attached cord. The cord makes an angle of 25 degrees with the horizontal. The block and surface have a coefficient of friction of .3. a) Find the value of the normal force. (Hint: It is not mg.) b) Find the x-component of the applied force. c) Find the value of the frictional force. d) Find Fnet in the x-direction. e) Does the block accelerate? If yes, what is the value of the acceleration?

 
 F-11 For now, a helicopter hovers motionless in air. Attached to the helicopter is cable 1 sthat supports block A (M = 200 kg). attached to block A is cable 2 which supports block B (M = 100kg). Find the tension on each cable if tthe helicopter a) is at rest. b) moves upward with a constant speed of 3 m/s; c) moves upward with an acceleration of 3 m/s^2.

 

F-12 Block B (M = 10 kg) rests on a table where u = .4. Blocb A is attached to to block B by a cord that is draped over a massless, frictionless pulley at the left side of the table. by similar arrangement, block C is attached at the right of block B. What must be the mass of block C if B is to accelerlate to the right at 4 m/s^2?

F-13 A block (m = 5 kg) is placed on an inclined plane (theta = 37^o). There is friction. (u = .4) a) What is the magnitude and direction of a separate force applied to the block to cause it to slide up the plane at a constant speed? b) What is the magnitude and direction of a separate force applied to the block to causes it to slide down the plane at a constant speed?

F-14 A block is projected up a 40^o incline at some speed. It eventually stops. For what range of values for u will the block stop and not move again?

 

 

 
 Figure 15  Figure 16   Figure 17 

15. See figure 15. It shows the blue block (m = 5 kg) resting on a surface where u = .5..What is the smallest possible value for the red mass that will cause the blue mass to slip. Note that the blue cable makes an angle of 30^o with vertical.

16. See figure 16. The sign iss held up and away from the building by the diagonal cable and horizontal boom. Find the force on each. (Note that the red cable makes an angle of 30^o with vertical.)

17. See figure 17. Two blocks are at rest on a 37^o incline. Red ( m = 2 kg, u = .4) and blue (m = 1 kg, u = .2) are connected by a rigid rod. The blocks are released. Find the acceleration if a)red precedes blue; b) blue precedes red.

see the applet at http://canu.ucalgary.ca/map/content/energy/energy_cons/simulate/fletcher/applet.html

 

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this page was last edited 01/23/09