Dynamics


Inclined Planes

A block of mass 5 kg is launched with an initial speed of 20 m/s rising over an inclined plane of 45°. There is no friction between the block and the inclined plane. Determine the distance that the block will come to rest.

Solution

Suggestion: compare with inclined plane with friction.

Two blocks, masses 3 kg and 2 kg, are released from the rest at the top of a 30° inclined plane and run over a distance of 40 m to the base of the plane, the plane is frictionless. Determine what block will arrive at the end with the highest speed.

Solution

 

Resistive Forces

On a windless day, a car travels at a constant speed of 72 km/h, the constant of the car shape c is equal to 0.6 SI units (International System of Units), and the perpendicular area to the direction of motion is 3 m2. Find the magnitude of the drag force.

Solution

A block of mass 5 kg, is launched with an initial speed of 20 m/s in ascending direction over an inclined plane of 45°. The coefficient of friction between the block and the plan is equal to 0.4. Determine the distance that the block will come to rest.

Solution

Recommendation: compare with inclined plane frictionless.

In the system of the figure bodies, A and B have masses of 20 kg and 10 kg. respectively. They are tied by a rope, and on the rope is fixed a spring scale, which reads that the force of tension on the cord is 100 N. Between the body A and the plane exists friction. The rope is inextensible and passes through a frictionless pulley and has negligible mass. Determine the acceleration of the system and the coefficient of friction between the block and the plane.

Solution

 

Newton’s Second Law Applied to Circular Motion

A high-speed train travels a 2500 m radius curve at a speed of 270 km/h, determine:
a) The centrifugal force felt by a passenger of a mass of 70 kg in a wagon;
b) What should be the speed of a car traveling a 10 m radius curve so that the passenger of the train feels the same centrifugal force being in the car? Answer in km/h.

Solution