тg Figure P4.64

A train car is accelerating with an unknown acceleration. There is a small mass hanging from a string that is attached to the ceiling of the train car. Because the train is accelerating forward, the mass is angled backwards at 6.4 deg. from the vertical. What is the magnitude of the train's acceleration?

A taut massless string connects two boxes as shown in the figure.  The boxes are placed on an incline plane at θ = 33.00.  What is the acceleration of boxes as they move down the incline, given m2 = 1.4 kg, m1 = 5.0 kg, μ2 = 0.10 and μ1 = 0.20.

A box, initially at rest, is pushed up a ramp that makes an angle of 15◦ with the horizontal as shown in the diagram. The magnitude of the pushing force is 8m newtons, where m is the mass of the box in kilograms. The force is in a direction parallel to and up the ramp. The coefficient of sliding friction between the box and the ramp is 0.25. Model the box as a particle and take the magnitude of the acceleration due to gravity to be g = 9.8 m s−2 . Express the four forces in component form in terms of unknown magnitudes where appropriate and find an expression for the resultant force acting on the box. Hence find the magnitude of the acceleration of the box, in m s−2

A 60 kg block slides along the top of a 100 kg block.  The lighter block has an acceleration of 3.8 m/s2 when a horizontal force F= 390 N is applied.  Assuming there is no friction between the bottom 100 kg block and the horizontal frictionless surface but there is friction between the blocks.  Find the acceleration of the 100 kg block during the time the 60 kg block remains in contact.

What If? How would your answers to parts (a) and (b) of this problem change if the 2.0 kg block was now stacked on top of the 1.0 kg block? Assume that the 2.0 kg block sticks to and does not slide on the 1.0 kg block when the system is accelerated. (Enter the acceleration in m/s2 to the right and the tension in N.)

54. Objects of masses m, = 4.00 kg and m, = 9.00 kg are connected by a light string that passes over a fric- tionless pulley as in Figure P4.54. The object m, is held m at rest on the floor, and m, rests on a fixed incline of 0 = 40.0°. The objects are released from rest, and m, slides 1.00 m down the incline in 4.00 s. Determine (a) the acceleration of each object, (b) the tension in the string, and (c) the coefficient of kinetic friction between m, and the Figure P4.54 incline.

Two packing crates of masses m, = 10.0 kg and m, = 4.90 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 4.90-kg crate lies on a smooth incline of angle 37.0°. Find the following. m2 m, (a) the acceleration of the 4.90-kg crate m/s? (up the incline) (b) the tension in the string