A man pushing a crate of mass  m = 92.0 kg  at a speed of  v = 0.860 m/s  encounters a rough horizontal surface of length  ℓ = 0.65 m  as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.360 and he exerts a constant horizontal force of 279 N on the crate. A man pushes a crate labeled m, which moves with a velocity vector v to the right, on a horizontal surface. The horizontal surface is textured from the right edge of the crate to a horizontal distance ℓ from the right edge of the crate. (a) Find the magnitude and direction of the net force on the crate while it is on the rough surface. magnitude  N direction     (b) Find the net work done on the crate while it is on the rough surface.  J (c) Find the speed of the crate when it reaches the end of the rough surface.  m/s

Two constant forces act on an object of mass m = 4.30 kg object moving in the xy plane as shown in the figure below. Force F, is 26.5 N at 35.0°, and force F, is 48.0 N at 150°. At time t = 0, the object is at the origin and has velocity (3.50î + 2.15j) m/s. 150° 35.0° (a) Express the two forces in unit-vector notation. F, - N (b) Find the total force exerted on the object. N (c) Find the object's acceleration. m/s2 Now, consider the instant t = 3.00 s. (d) Find the object's velocity. m/s (e) Find its position. (f) Find its kinetic energy from V½mv2. kJ (g) Find its kinetic energy from 2mv,2 + EF · AF. kJ

The figure shows a block of mass m resting on a 20° slope. The block has coefficients of friction μs = 0.64 and μk = 0.54 with the surface of the slope. It is connected using a very light string over an ideal pulley to a hanging block of mass 2.0 kg. The string above the slope pulls parallel to the surface. What is the minimum mass m so the system will remain at rest when it is released from rest?

A force in the +x-direction with magnitude F(x) = 18.0 N - (0.530 N/m)x is applied to a 8.30 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.