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Tension - Equilibrium and Elasticity: Five problems

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1. The system in the picture is in equilibruim with the string in the center exactly horizontal. Find (a) tension T 1 , (b) tension T 2 (c) tension T 3 (d) angel pheta

2. The system in the picture is in equilibrium. A concrete block of mass 225 kg hanfs from the end of the uniform strut whose mass is 45.0 kg. Find (a) the tension T in the cable and the (b) horizontal and (c) vertical force components on the strut from the hinge.

3. For the step ladder shown in the picture. Sides AC and CE are each 2.44 m long and hinged at C. Bar BD is a tie-rod 0.762 m long , halfway up. A man weighing 854 Newtons climbs 1.80 m along the ladder assuming that the floor is frictionless and neglect ing the mass of the ladder, find (a) the tension in the tie-rod and the magnitudes of the forces on the ladder from the floor at (b) A and (c) E

4. A construction worker attempts to lift a uniform beam off the floor and raise it to a vertical position. The beam is 2.5 m long and weighs 500 N. At a certain instant the worker hold the beam momentarily at rest with one end 1.5m off the floor as shown in the figure below by exerting a force vector P on the beam, perpendicular to the beam. (a) what's the magnitude of the force exerted by the worker ? (b) What is the magnitude of the (net) force of the floor on the beam? (c) What is the minimum value that the coefficient of static friction between the beam and the floor can have in order for the beam not to slip at this instant ?

5. The picture shows a uniform ramp between two buildings that allows for motion between the buildings due to strong winds. At its left end it is hinged to the building wall, at its right end it has a roller that can roll along the building wall. There is no vertical force on the roller from the building, only a horizontal force with magnitude Fh . The horizontal distance between the buildings is D=4.00 m . The rise of the ramp is h= 0.490m. A man walks across the ramp from the left Picture 5-1 gives Fh as a function of horizontal distance x of the man from the building at the left. What are the masses of (a) the ramp and (b) the man ?

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1. There is typo, in two strings you have written T2, hence, I've considered T3 in horizontal string and T2 in the string inclined at Q (read as theta) with respect to vertical.

For whole system:
Equlibrium in vertical direction: sum(Fv) = 0
T1*cos(35) + T2*cos(Q) = 40+50 = 90 ....(1)
(Here Q read as theta)
In horizontal direction:
T1*
538.516sin(35)-T2*sin(Q) = 0 ......(2)
At the junction of T1, T3 (horizontal st
ring) and 40 N, by sine law:
T1/sin(90) = T3/sin(180-35) = 40/sin(90+35)
=> T1 = T3*1.74 = 40*1.22 = 48.8
=> T1 = 48.8 N --Answer
T3 = 48.8/1.74 = 28.05 N (horizontal string) --Answer
From equation 2:
T2*sin(Q) = T1*sin(35) = 48.8*0.574 = 28.01 ....(3)
From ...

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17 Problems All in Mechanics: Force, tension, energy, vel...

Question 1: A packing crate is placed on a plane inclined at an angle of 35o from horizontal. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.

Question 2: For the situation shown in the figure, what is the minimum coefficient of static friction between the block and the surface that will keep the block from moving? (F1 = 5.0 N, F2 = 4.0 N, and m = 5.0 kg.)

Question 3: If the coefficient of kinetic friction between the block and the table in the figure below is 0.560, and m1 = 0.150 kg and m2 = 0.250 kg (a) what should m3 be if the system is to move with a constant speed? (b) If m3 = 0.100 kg, what is the magnitude of the acceleration of the system? (Assume ideal conditions for the string and pulleys.)

Question 4 A father pulls his young daughter on a sled with a constant velocity on a level surface through a distance of 10 m, as illustrated below. If the total mass of the sled and the girl is 35 kg and the coefficient of kinetic friction between the sled runners and the snow is 0.20, how much work does the father do?

Question 5: A student could either pull or push, at an angle of 30o from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m.
(a) Compared with pushing, pulling requires the student to do (1) less, (2) the same, or (3) more work.
(b) Calculate the minimum work required for both pulling and pushing.

Question 6: A particular spring has a force constant of 2.5 X 103 N/m.
(a) How much work is done in stretching the initially-relaxed spring by 6.0 cm?
(b) How much more work is done in stretching the spring an additional 2.0 cm?

Question 7: Levers, pulleys, and wedges are simple machines. Does the concept of work explain why we use these machines in our daily lives, how they work, and why they work? Explain your reasons in two paragraphs, taking examples from daily life.

Question 8: For identical materials, the static coefficient cannot be greater than kinetic

True or False

Question 9: A wooden block slides directly down an incline plane, at constant velocity of 6.0 m/s. How large is the coefficient of the kinetic friction, if the plane makes an angle of 25 degrees with the horizontal?

A. 0.47
B. 0.42
C. 0.91
D. 0.37
E. 2.1

Question 10: Consider a plot of the displacement on the y- axis vs. applied force on the x-axis for an ideal elastic spring. The slope of the curve would be:
A. the spring is constant
B. the reciprocal of the spring constant
C. the reciprocal of the acceleration of gravity
D. the acceleration of gravity

Question 11: You lift a 10. lb physic book up in the air a distance of 1 ft., at a constant velocity of 0.5 ft./s the work is done by gravity.
A. Zero
B. +5 ft. lb.
C. +10 ft. lb
D. - 10 ft. lb
E. - 5 ft. lb

Question 12: To push a piece of heavy furniture across the carpet usually takes more force to get it moving than it takes to keep it moving. That is because
A. the kinetic coefficient of friction is larger than static coefficient
B. of Newton's Third Law
C. It does not take more force
D. The static coefficient of friction is larger than kinetic coefficient

Question 13: The kinetic friction of one metal object sliding along another metal surface depend least upon.
A. the coefficient of kinetic friction
B. the normal force
C. the nature of the materials in contact
D. the area of contact

Question 14: A packing car slides down an incline at a constant velocity. Thus we can deduce that:
A. a net downward force is acting on it
B. it may be accelerating
C. a frictional force is acting on it
D. it is not acted on by an appreciable gravitational force

Question 15: Which of the following is not an unit of work
A. N-m
B. KW-h
C. J
D. W-s
E. Kg-m/s

Question 16: Two men, Joel and Jerry , push against a immovable wall. Jerry stops at 10 minutes , while Joel is able to push another 5 minutes longer. Compare the work they do:
A. Jerry does 50% more work than Joel
B. Joel does 50% more work than Jerry
C. Neither of them do anymore work
D. Joel does 75% more work than Jerry

Question 17: A 10.0 Kg mass, hung onto a spring , causes the spring to stretch 2.0 cm. the spring is constant is:
A. 0.020 N/cm.
B. 49 N/cm
C. 20.0 N/cm
D. 5.0 N/cm
E. 0.20 N/cm

See Attach Word doc file for additional information.

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