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dynamics Dynamics 3
In this pulley system, block A is moving downward with a speed of 4 ft/s while block C is moving up at 2 ft/s. Find the speed of block B.
Given v(a)=650 km/h and v(b)=800 km/h, find v(b/a). Two airplanes are traveling towards each other, traveling at 650 km/h and 800 km/h.
The platform is rotating about the vertical axis such that at any instant its angular position is theta=4(t^(3/2)) rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r=.1(t^3) m, where t is in seconds. Determine the magnitude of the velocity and acceleration of the ball when t=1.5 s.
A particle moves along a circular path of radius 300 mm. If its angular velocity is theta dot=3(t^2) rad/s, where t is in seconds, determine the magnitude of the particle's velocity when theta=45 degrees. The particle starts from rest when theta=0 degrees. Determine the magnitude of the particle's acceleration.
The driver of the car maintains a constant speed of 22 m/s. Determine the angular velocity of the camera tracking the car when theta=15 degrees.
The casting has a mass of 3 Mg. Suspended in a vertical position and initially at rest, it is given an upward speed of 200 mm/s in .3 s using the crane hook H. Determine the tension in cables AC and AB during this time interval if the acceleration is constant.
The crate has a mass of 80 kg and is being towed by a chain which is always directed 20 degrees from the horizontal as shown. Determine the crate's acceleration in t=2 s if the coefficient of static friction is .4, the coefficient of kinetic friction is .3 and the towing force is P=90(t^2) N, where t is in seconds.
If a horizontal force of P=10 lb is applied to block A, determine the acceleration of block B. Neglect friction. Hint: show that a(B)=a(A)tan(15).
Given v(a)=650 km/h and v(b)=800 km/h, find v(b/a). Two airplanes are traveling towards each other, traveling at 650 km/h and 800 km/h.
The platform is rotating about the vertical axis such that at any instant its angular position is theta=4(t^(3/2)) rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r=.1(t^3) m, where t is in seconds. Determine the magnitude of the velocity and acceleration of the ball when t=1.5 s.
A particle moves along a circular path of radius 300 mm. If its angular velocity is theta dot=3(t^2) rad/s, where t is in seconds, determine the magnitude of the particle's velocity when theta=45 degrees. The particle starts from rest when theta=0 degrees. Determine the magnitude of the particle's acceleration.
The driver of the car maintains a constant speed of 22 m/s. Determine the angular velocity of the camera tracking the car when theta=15 degrees.
The casting has a mass of 3 Mg. Suspended in a vertical position and initially at rest, it is given an upward speed of 200 mm/s in .3 s using the crane hook H. Determine the tension in cables AC and AB during this time interval if the acceleration is constant.
The crate has a mass of 80 kg and is being towed by a chain which is always directed 20 degrees from the horizontal as shown. Determine the crate's acceleration in t=2 s if the coefficient of static friction is .4, the coefficient of kinetic friction is .3 and the towing force is P=90(t^2) N, where t is in seconds.
If a horizontal force of P=10 lb is applied to block A, determine the acceleration of block B. Neglect friction. Hint: show that a(B)=a(A)tan(15).
At the instant shown, the 50-kg projectile travels in the vertical plane with a speed of v=40 m/s. Determine the tangential component of its acceleration and the radius of curvature of its trajectory at this instant.
A spring, having an unstretched length of 2 ft, has one end attached to the 10-lb ball. Determine the angle theta of the spring if the ball has a speed of 6 ft/s tangent to the horizontal circular path.
Determine the minimum coefficient of static friction between the tires and the road surface so that the 1.5 Mg car does not slide as it travels at 89 km/h on the curved road. Neglect the size of the car.
A 5 Mg airplane is flying at a constant speed of 350 km/h along a horizontal circular path. If the banking angle theta=15 degrees, determine the uplift force L acting on the airplane and the radius r of the circular path. Neglect the size of the airplane.
The path motion of a 5 lb particle in the horizontal plane is described in terms of polar coordinates as r=(2t+1) ft and theta=(.05(t^2)-t) rad, where t is in seconds. Determine the magnitude of the resultant force acting on the particle when t=2s.
The 5 lb box is projected with a speed of 20 ft/s at A up the vertical circular smooth track. Determine the angle theta when the box leaves the track.
The 10 lb block travels to the right at v(a)=2 ft/s at the instant shown. If the coefficient of kinetic friction is .2 between the surface and A, determine the velocity of A when it has moved 4 ft. Block B has a weight of 20 lb.
At the instant theta=45 degrees, the boy with a mass of 75 kg, moves a speed of 6 m/s, which is increasing at .5 m/s^2. Neglect his size and the mass of the seat and chords. The seat is pin connected to the frame BC. Find the horizontal and vertical reactions of the seat on the boy.
A spring, having an unstretched length of 2 ft, has one end attached to the 10-lb ball. Determine the angle theta of the spring if the ball has a speed of 6 ft/s tangent to the horizontal circular path.
Determine the minimum coefficient of static friction between the tires and the road surface so that the 1.5 Mg car does not slide as it travels at 89 km/h on the curved road. Neglect the size of the car.
A 5 Mg airplane is flying at a constant speed of 350 km/h along a horizontal circular path. If the banking angle theta=15 degrees, determine the uplift force L acting on the airplane and the radius r of the circular path. Neglect the size of the airplane.
The path motion of a 5 lb particle in the horizontal plane is described in terms of polar coordinates as r=(2t+1) ft and theta=(.05(t^2)-t) rad, where t is in seconds. Determine the magnitude of the resultant force acting on the particle when t=2s.
The 5 lb box is projected with a speed of 20 ft/s at A up the vertical circular smooth track. Determine the angle theta when the box leaves the track.
The 10 lb block travels to the right at v(a)=2 ft/s at the instant shown. If the coefficient of kinetic friction is .2 between the surface and A, determine the velocity of A when it has moved 4 ft. Block B has a weight of 20 lb.
At the instant theta=45 degrees, the boy with a mass of 75 kg, moves a speed of 6 m/s, which is increasing at .5 m/s^2. Neglect his size and the mass of the seat and chords. The seat is pin connected to the frame BC. Find the horizontal and vertical reactions of the seat on the boy.
A 800 kg car is traveling over the hill having the shape of a parabola. When it is at point A, it is traveling at 9 m/s and increasing its speed at 3 m/s^2. Find the resultant normal force and resultant fricional force exerted on the road at point A.
The 2 kg block B and the 15 kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block travels along a circular path of radius r=1.5 m, determine the speed of the block.
An acrobat has a weight of 150 lb and is sitting on a chair which is perched on top of a pole as shown. If by a mechanical drive the pole rotates downward at a constant rate from theta=0 degrees, such that the acrobat's center of mass G maintains a constant speed of v(a)=10 ft/s, determine the angle theta at which he begins to fly out of the chair. Neglect friction and assume that the distance from one pivot O to G is 15 ft.
If the 10 lb block A slides down the plane with a constant velocity when theta=30 degrees, determine the acceleration of the block when theta = 45 degrees.
The 75 kg man climbs up the rope with an acceleration of .25 m/s^2, measured relative to the rope. Determine the tension on the rope and the acceleration of the 80 kg block.
Determine the required mass of block A so that when it is released from rest it moves the 5 kg block B a distance of .75 m up along the smooth inclined plane in t=2s. Neglect the mass of the pulleys and cords.
Determine the maximum speed attained by the 1.5 Mg rocket sled if the rockets provide the thrust shown in the graph. Initially, the sled is at rest. Neglect friction and the loss of mass due to fuel consumption.
The 10 kg smooth block moves to the right with a velocity of v(0)=3 m/s when force F is applied. If the force varies as shown in the graph, determine the velocity of the block when t=4.5 s.
The winch delivers a horizontal towing force F to its cable at A which varies as shown in the graph. Determine the speed of the 80 kg bucket when t=24 s. Originally the bucket is released from rest.
The 2 kg block B and the 15 kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block travels along a circular path of radius r=1.5 m, determine the speed of the block.
An acrobat has a weight of 150 lb and is sitting on a chair which is perched on top of a pole as shown. If by a mechanical drive the pole rotates downward at a constant rate from theta=0 degrees, such that the acrobat's center of mass G maintains a constant speed of v(a)=10 ft/s, determine the angle theta at which he begins to fly out of the chair. Neglect friction and assume that the distance from one pivot O to G is 15 ft.
If the 10 lb block A slides down the plane with a constant velocity when theta=30 degrees, determine the acceleration of the block when theta = 45 degrees.
The 75 kg man climbs up the rope with an acceleration of .25 m/s^2, measured relative to the rope. Determine the tension on the rope and the acceleration of the 80 kg block.
Determine the required mass of block A so that when it is released from rest it moves the 5 kg block B a distance of .75 m up along the smooth inclined plane in t=2s. Neglect the mass of the pulleys and cords.
Determine the maximum speed attained by the 1.5 Mg rocket sled if the rockets provide the thrust shown in the graph. Initially, the sled is at rest. Neglect friction and the loss of mass due to fuel consumption.
The 10 kg smooth block moves to the right with a velocity of v(0)=3 m/s when force F is applied. If the force varies as shown in the graph, determine the velocity of the block when t=4.5 s.
The winch delivers a horizontal towing force F to its cable at A which varies as shown in the graph. Determine the speed of the 80 kg bucket when t=24 s. Originally the bucket is released from rest.
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