Dynamics
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Newton’s Second Law Applied to Circular Motion
A car, considered a point, with mass m turns around a circular runway of radius R. The
coefficient of friction between road and tires is μ. Assume g for the acceleration due to
gravity. Determine the maximum speed that the car may have in the curve without slipping.
A small mass m is placed into a container whose inner surface is a hemisphere of radius R.
The container rotates around the vertical axis with angular velocity ω. Determine:
a) The magnitude of the force that the sphere makes against the wall;
b) The radius of the circumference described by the sphere when in equilibrium to the container.
a) The magnitude of the force that the sphere makes against the wall;
b) The radius of the circumference described by the sphere when in equilibrium to the container.
A car runs on a banked curve with radius R and slope θ. What will be the maximum speed to
negotiate the curve without friction?
A cylinder has the axis in the vertical direction and radius R, spinning inside the cylinder in a
horizontal plane there is a small sphere. Assuming that the coefficient of friction between the sphere and
the wall of the cylinder is μ and the local acceleration due to gravity is g, calculate the
minimum tangential speed of the particle spinning inside the cylinder without falling.
A rod with length L is leaning at an angle θ relative to the vertical. In the rod, there is
a ring that can slide without friction. The system is rotating around a vertical axis through the lower
end with constant angular velocity. Determine angular velocity that must be carried out by the rod so
that the ring remains at rest in the midpoint of the rod.
A car with mass m passes through a speed bump, represented by a circumference arc with a radius
equal to R, with constant speed. Assuming the acceleration due to gravity equal to g,
determine:
a) The reaction force of the road on the car at the highest point of the speed bump;
b) The maximum speed that the car can have at the highest point of the speed bump without the wheels losing contact with the road.
a) The reaction force of the road on the car at the highest point of the speed bump;
b) The maximum speed that the car can have at the highest point of the speed bump without the wheels losing contact with the road.
Miscellaneous
The bodies A and B have masses of 3m and 2m respectively and slide
without friction over the horizontal plane, the body C, hanging on the rope, has mass
m. Consider that the rope has a negligible mass, the pulley is without friction, and the
gravitational acceleration is g. Calculate the magnitudes of:
a) The acceleration of the body C;
b) The force of reaction of body B on A.
a) The acceleration of the body C;
b) The force of reaction of body B on A.
The fiure represents a system is composed of an elevator of mass M and a mass of mass
m. The elevator is hanging by a rope that passes through a fixed pulley and comes to the
operator's hands, the rope and the pulley are supposed frictionless and have a negligible mass.
The operator pulls the rope and rises with constant acceleration a along with the
elevator. It is assumed known M, m, a, and g. Determine the force
that the elevator exerts on the operator.
Three bodies A, B, and C are suspended by inextensible cords as shown in the figure.
Body B is simultaneously suspended by two cords, one connected to body A and another to
body C. Determine:
a) Acceleration and direction of motion if all masses are equal to m;
b) Acceleration and direction of motion, if the masses A and C are equal to m and mass B equal to 3m;
c) If the masses A and C are equal to m, what should be the value of mass B for the movement to give upwards with an acceleration equal to 0.5g?
a) Acceleration and direction of motion if all masses are equal to m;
b) Acceleration and direction of motion, if the masses A and C are equal to m and mass B equal to 3m;
c) If the masses A and C are equal to m, what should be the value of mass B for the movement to give upwards with an acceleration equal to 0.5g?
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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .