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Problem #1
(a) What force is needed to accelerate a sled (total mass = 65 kg ) at 1.50 m/s2 on horizontal frictionless ice. (b) A 14.0 kg bucket is lowered vertically by a rope in which there is 160 N
of tension at a given instant. Determine the acceleration.
(a)
N
Answer part (a)
(b)
m/s2
Answer part (b)
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Problem #2
Two blocks with masses M1 = 5.30 kg and M2 = 7.30 kg hang one under the other as shown in the diagram. (a) Assuming the blocks are at rest, find T2, the tension in the lower rope.
(b) Assuming the blocks are at rest, find T1 , the tension in the upper rope. (c) If we now assume the blocks are accelerating 4.60 m/s2 upward, find T2. (d) Still assuming that the blocks
are accelerating 4.60 m/s2 upward, find T1.
(a)
N
Answer part (a)
(b)
N
Answer part (b)
(c)
N
Answer part (c)
(d)
N
Answer part (d)
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Problem #3
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A block with mass mA = 10.0 kg on a smooth horizontal surface is connected by a thin cord that passes over a pulley to a second block with mass mB = 4.20 kg which hangs vertically
as shown in the figure. (a) Determine the magnitude of the acceleration of the system. (b) If initially mA is at rest 1.25 m from the edge of the table, how long does it take to reach the
edge of the table if the system is allowed to move freely?
(a)
m/s2
Answer part (a)
(b)
s
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Problem #4
A 25.0 kg block is connected to an empty 3.80 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.43 and the
coefficient of kinetic friction between the table and the block is 0.23. Sand is gradually added to the bucket until the system just begins to move. Ignore the mass of the cord. (a)
Calculate the mass of sand added to the bucket. (b) Calculate the acceleration of the system.
(a)
kg
Answer part (a)
(b)
m/s2
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Problem #5
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A person is pulling a 27.5 kg box at the end of a rope making an angle of 27.8o above the horizon as shown in the diagram. If the person is slowly increasing the applied force, F, and
the box begins to move when the applied force is 65.5 N, then what is the coefficient of static friction?
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Problem #6
A block that has a mass of 44.3kg hangs from a rope that is connected to two additional ropes as depicted in the above figure. The angles θ1 and θ2 have the respective values 35.9o and
48.7o . Assuming that the rope masses are negligible, what are values of (a) |T1 |, (b) |T2|, and (c) |T3|? (d) Assuming that the system is now on the moon with gm = 1.63m/s2, what is the
value now for |T2|?
(a)
N
Answer part (a)
(b)
N
Answer part (b)
(c)
N
Answer part (c)
(d)
N
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Problem #7
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Three blocks with masses m1 = 4.08kg, m2 = 2.07kg, and m3 = 17.3kg are shown in the above diagram. What must the value of the force, F, be to keep m1 and m2 stationary with
respect to m3? Assume all surfaces are frictionless.
N
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Problem #8
Two blocks with masses m1 = 8.4kg and m2 = 15.5kg are connected by a system of pulleys as shown in the above diagram. Find the (a) magnitude of the acceleration. Assuming that
the string and pulley masses are negligible, we know that T1 = T2 = T3 = T4. (b) Find T4.
(a)
m/s2
Answer part (a)
(b)
N
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Problem #9
What is the magnitude of the average force required to stop a 1400 kg car in 6.00 s if it is initially traveling at 80 km/h?
N
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Problem #10
A block of mass 3.64 kg is on an incline plane that makes an angle θ = 31.2o with the horizonal. The block and inclined plane have a coefficient of kinetic friction, µk. (a) What is the
magnitude of the normal force? (b) If the block is sliding down the ramp at constant velocity, then what is the coefficient of kinetic friction?
(a)
N
(b)
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Problem #11
A woman stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 65% of her regular weight. Calculate the magnitude of
acceleration of the elevator.
N
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Problem #12
The coefficient of static friction between hard rubber and normal street pavement is about 0.78. On how steep a hill can you leave a car parked (what is the maximum angle)?
o
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Problem #13
The pulley in is suspended by a cord C. Suppose that m1 = 2.70 kg and m2 = 4.50 kg. Determine the tension in the cord that supports the pulley C after the masses are released.
N
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Problem #14
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Suppose the coefficient of kinetic friction between mA and the plane, shown in the figure is 0.23, and that mA = mB = 2.4 kg. Ignore masses of the frictionless pulley and the cord, and
take the angle θ to be 37o. (a) Determine the magnitude of the acceleration of the system of masses. (b) Determine the smallest value of µk that would keep the system of masses from
accelerating.
(a)
(b)
m/s2
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