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ENGINEERING MECHANICS-DYNAMICS An auto,equipped with only wheel brakes, has a wheelbase of 120 in. with its c.g. located 60 in. ahead of the rear wheels and 36 in. above the pavement. If f = 0.80 at the tires, compute the minimum distance in which the auto can be brought to rest from a speed of 60 mph if the driver’s reaction time before applying the brakes is 3/4 sec.

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ENGINEERING MECHANICS-DYNAMICS A car with a four-wheel drive weighs 3000lb and has a wheelbase of 10 ft. The c.g. is 3 ft above the pavement and 4 ft ahead of the rear wheels. Compute the tractive force acting at the rear wheels when the car accelerates at 1/3 g ft per sec 2. Assume the coefficient of friction is equal at all four wheels.

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ENGINEERING MECHANICS-DYNAMICS The coefficient of kinetic friction under the sliding supports at A and B in Fig. P-1083 is 0.30. What force P will give the 600-lb door a leftward acceleration of 8.05 ft per sec 2 ? What will be the normal pressures at A and B?

Repeat Prob. 1083 if f = 0.30 at A and f = 0.20 at B. ROTATION

ENGINEERING MECHANICS-DYNAMICS

In Fig. P-1085, Find the angle

θ at which a uniform bar will be maintained inside the

smooth surface of a cylindrical drum accelerating leftward at 3/5 g ft per sec 2. ROTATION

ENGINEERING MECHANICS-DYNAMICS

A bar weighing 2 lb per ft is bent at right angles into segments 26 in. and 13 in. long. It takes the position shown in Fig P-1086 when the frame F to which it is pinned at A is accelerated horizontally. Determine this acceleration and the components of the reaction at A.

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ENGINEERING MECHANICS-DYNAMICS

The uniform crate shown in Fig. P-1087 weighs 200 lb. It is pulled up the incline by a counterweight W of 400 lb. Find the maximum and minimum values of d so that the crate does not tip over as it slides up the incline.

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ENGINEERING MECHANICS-DYNAMICS

Determine the value of W in Prob. 1087 if the 200-lb crate is on the verge of tipping forward as it slides up the incline. Assume d = 3.32 ft.

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ENGINEERING MECHANICS-DYNAMICS

The frame of a machine is accelerated leftwards at 3/5 g ft per sec 2. As shown in Fig. P1089, it carries a uniform angle ABC weighing 80 lb which is braced by the uniform strut Cd weighing 60 lb. Determine the components of the pin pressure at C upon CD.

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ENGINEERING MECHANICS-DYNAMICS

Repeat Prob. 1089 if the frame of the machine is accelerated rightwards at 4/5 g ft per 2

sec .

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ENGINEERING MECHANICS-DYNAMICS

The uniform bar AB weighing 240 lb is mounted as shown in Fig. P-1091 upon a carriage weighing 480 lb. The center of gravity of the carriage is at C midway between the wheels. If P = 180 lb and there is no frictional resistance at the wheels, find R 1 and R2 and also the horizontal and vertical components of the pin pressure at A.

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ENGINEERING MECHANICS-DYNAMICS

Repeat Prob. 1091 if the magnitude and sense of P is such that the reaction of the carriage upon the bar at B is 60 lb leftwards.

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ENGINEERING MECHANICS-DYNAMICS

Two bodies A and B, each weighing 96.6 lb,are connected by a rigid bar of negligible weight attached to them at their gravity centers. The coefficients of reaction of the wall and floor reactions. Explain why these reactions pass though the gravity center of B and A respectively. Hint: Relate the acceleration by the method developed in Illus. Prob. 1018 on p. 258.

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ENGINEERING MECHANICS-DYNAMICS

Repeat Prob. 1093 if a leftward horizontal force of 180 lb is applied to body A.

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ENGINEERING MECHANICS-DYNAMICS

The initial angular velocity of the compound pulley B in the figure is 6 rad per sec counterclockwise and weight D is decelerating at the constant rate of 4 ft per sec 2. What distance will weight A travel before coming to rest?

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ENGINEERING MECHANICS-DYNAMICS

A flywheel 6 ft in diameter accelerates from rest at the constant rate of 4 rpm per sec. Compute the normal and tangential components of the acceleration of a particle on the rim of the flywheel after 10 sec.

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ENGINEERING MECHANICS-DYNAMICS

The rim of a 50-in wheel on a brakeshoe testing machine has a speed of 60 mph when the brake is dropped. It comes to rest after the rim has traveled a linear distance of 6000 ft. What are the constant angular acceleration and the number of revolutions the wheel makes in coming to rest?

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ENGINEERING MECHANICS-DYNAMICS

A gear is accelerated from rest to a speed of 900 rpm and then immediately decelerated to a stop. If the total elapsed time is 10 sec, determine the total number of revolutions of the gear. Assume that both acceleration and deceleration are constant but not necessarily of the same magnitude.

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ENGINEERING MECHANICS-DYNAMICS

When the angular velocity of a 4-ft diameter pulley is 3 rad per sec, the total acceleration of a point on its rim is 30 ft per sec2. Determine the angular acceleration of the pulley at this instant.

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ENGINEERING MECHANICS-DYNAMICS

Determine the horizontal and vertical components of the acceleration of point B on the rim of the flywheel shown in the figure. At the position, ω= 4 rad per sec and ɑ= 12 rad per sec 2, both clockwise.

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ENGINEERING MECHANICS-DYNAMICS

Repeat prob. 1206 except that a ɑ is changed to 10 rad per sec 2 counterclockwise.

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ENGINEERING MECHANICS-DYNAMICS

A pulley has a constant angular acceleration of 3 rad per sec 2. When the angular velocity is 2 rad per sec, the total acceleration of a point on the rim of the pulley is 10 ft per sec 2. Compute the diameter of the pulley.

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ENGINEERING MECHANICS-DYNAMICS

The step pulleys shown in the figure are connected by a cross belt. If the angular acceleration of C is 2 rad per sec2, what time is required for A to travel 180 ft from rest? Through what distance will D move while A is moving 240 ft?

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ENGINEERING MECHANICS-DYNAMICS

Repeat prob. 1209 if the radii of pulley B are changed to 30 in. and 18 in.

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ENGINEERING MECHANICS-DYNAMICS

The rod BO in the figure rotates in a vertical plane about a horizontal axis at O. At the given position, end B has a downward vertical component of velocity of 6 ft per sec and also a downward vertical component of 9 ft per sec2. Compute the angular acceleration of rod BO and the total acceleration of point A.

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ENGINEERING MECHANICS-DYNAMICS

A body rotates according to the relation ɑ= 3t2+4, displacement being measured in radians and time in seconds. If its initial angular velocity is 4 rad per sec and the initial angular displacement is zero, compute the values of ω and ϴ for the instant when t= 3 sec.

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ENGINEERING MECHANICS-DYNAMICS

The rotation of a pulley is defined by the relation ϴ= 2t 4-30t2+6, where ϴ is measured in radians and t in seconds. Compute the values of angular velocity and angular acceleration at the instant when t= 4 sec.

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ENGINEERING MECHANICS-DYNAMICS

The rotation of a flywheel is governed by the equation ω= 4 √ t

;ω is in radians per

second and t is in seconds. ϴ= 2 rad when t= 1 sec. Compute the values of ϴ and ɑ at the instant when t= 3 sec.

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ENGINEERING MECHANICS-DYNAMICS

A body rotates according to the relation ɑ= 2t, where ɑ is in radians per second and t is in seconds. ω= 4 rad per sec and ϴ is zero when t is zero. Compute the values of ω and ϴ at the instant when t= 2 sec.

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ENGINEERING MECHANICS-DYNAMICS

Determine the number of revolutions through which a pulley will rotate from rest if its angular acceleration is increased uniformly from zero to 12 rad per sec 2 during 4 sec and then uniformly decreased to 4 rad per sec2 during the next 3 sec.

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