Linear Mom
A 20-lb block slides down a 30° inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane is 0.25.
29.4 ft/s
The small cylinder C has a mass of 10 kg and is attached to the end of a rod whose mass may be neglected. If the frame is subjected to a couple moment M = (8t2 +5) N-m where t is in seconds, and the cylinder is subjected to a force of 60 N, which is always directed as shown, determine the speed of
the cylinder when The cylinder has a speed
v0 = 2 m>s when t = 0.
t = 2 s.
13.4 m/s
The bus B has a weight of 15000-lb and is traveling to the right at 5 ft/s. Meanwhile a 3000-lb car A is traveling at 4 ft/s to the left. If the vehicles crash head-on and become entangled, determine their common velocity just after the collision. Assume that the vehicles are free to roll during collision.
3.5 ft/s to the right
A flywheel has its angular speed increased uniformly from 15 rad/s to 60 rad/s in 80 s. If the diameter of the wheel is 2 ft, determine the acceleration of a point on the rim of the wheel when t = 80 s.
at = 0.562 ft/s2
an = 3600 ft/s2
A hammer head having a weight of 0.25 lb is moving vertically downward at 40 ft/s when it strikes the head of a nail of negligible mass and drives it into a block of wood. Find the impulse on the nail if it is assumed that the grip is loose, the handle has a negligible mass, and the hammer stays in contact with the nail while it comes to rest. Neglect the impulse caused by the weight of the hammer head during contact with the nail.
0.311 lb-s
A man hits the 50-g golf ball such that it leaves the tee at an angle of 40° with the horizontal and strikes the ground at the same elevation a distance of 20 m away. Determine the impulse of the club on the ball. Neglect the impulse caused by the ball’s weight while the club is striking the ball.
0.706 N-s.
The 10-lb block rests on a surface for which the coefficient of kinetic friction is 0.5. It is acted upon by a radial force of 2 lb and a horizontal force of 7 lb, always directed at 30° from the tangent to the path. If the block is initially moving in a circular path with a speed of 2 ft/s at the instant the forces are applied, determine the time required before the tension in cord AB becomes 20 lb. Neglect the size of the block for the calculation.
The 200-g projectile is fired with a velocity of 900 m/s towards the center of the 15-kg wooden block. If the projectile penetrates and emerges from the block with a velocity of 300 m/s, determine the velocity of the block just after the projectile emerges.
8 m/s to the right
A mill in a textile plant uses the belt-and-pulley arrangement shown to transmit power. When t = 0 s an electric motor is turning pulley A with an angular velocity of 5 rad/s. If this pulley is subjected to a constant angular acceleration 2 rad/s2 determine the angular velocity of pulley B after B turns 6 revolutions. The hub at D is rigidly connected to pulley C and turns with it.
10.6 rad/s
A tugboat is moving a barge by a rope. If it takes 35 s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest. The propeller provides the propulsion force F which gives the tugboat forward motion, whereas the barge moves freely. Determine F acting on the tugboat.The barge has a mass of 75 Mg.
24.8 kN
The crate B and cylinder A have a mass of 200 kg and 75 kg, respectively. If the system is released from rest, determine the speed of the crate when t = 3 s. Neglect the mass of the pulleys.
2.10 m/s
The four 5-lb spheres are rigidly attached to the crossbar frame having a negligible weight. If a couple moment M = (0.5t + 0.8) lb-ft, where t is in seconds, is applied, determine the speed of each of the spheres in 4 seconds starting from rest. Neglect the size of the spheres.
19.3 ft/s
The 5-Mg truck and 2-Mg car are traveling with the free rolling velocities of 30 km/h and 10 km/h to the right, respectively, just before they collide. After the collision, the car moves with a velocity of 15 km/h to the right relative to the truck. Determine the coefficient of restitution between the truck and car.
0.75
The crankshaft AB is rotating at a constant angular velocity of 150 rad/s. Determine the velocity of the piston P at the instant theta = 30°.
18.5 ft/s to the left
The 150-lb car of an amusement park ride is connected to a rotating telescopic boom.When r = 15 ft, the car is moving on a horizontal circular path with a speed of 30 ft/s. If the boom is shortened at a rate of 3 ft/s, determine the speed of the car when r = 10 ft.
45.1 ft/s