You push a 5.1kg cart along the floor with an unknown force F at 30° below the horizontal. Using a scale, you know the Normal force is 70N. What is the horizontal acceleration of the cart?

A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (b) parallel to the floor.

A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel to the incline

An 85,000 kg stunt plane performs a loop-the-loop, flying in a 260-m-diameter vertical circle. At the point where the plane is flying straight down, its speed is 55 m/s and it is speeding up at a rate of 12 m/s per second. (b) What angle does the net force make with the horizontal? Let an angle above horizontal be positive and an angle below horizontal be negative.

A particle is acted upon by 3 forces: a $10\mathrm{N}$ force in the positive x direction, a $20\mathrm{N}$ force in the positive y direction, and an unknown force. If the particle is in equilibrium, what is the magnitude of the unknown force?

A $500\mathrm{kg}$ car is parked on a hill with a 5° slope. What is the magnitude of the friction force acting on the car?

A curve on an unbanked highway has a radius of 300 m. What minimum coefficient of static friction is required for a car to make the corner at $29\mathrm{m}/\mathrm{s}$ (about $65\mathrm{mph}$).

A race track has turns of radius $400\mathrm{m}$ that are banked at 30° above the horizontal. What is the fastest a car could go around this corner with no assistance from friction?