Dynamics
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Basic Concepts
A box of mass m is on a horizontal surface, the coefficient of kinetic friction between the box
and surface is μ. A force
\( \vec{F} \)
is applied making an angle α with the horizontal.
a) For what value of the angle α, the acceleration of the box is maximum?
b) For what values of α the box remains at rest?
a) For what value of the angle α, the acceleration of the box is maximum?
b) For what values of α the box remains at rest?
Inclined Planes
Two blocks, with masses mA and mB, are released from the rest on very
long inclined planes. Block A is on a plane that makes an angle α with the horizontal, and
block B is on a plane with an angle β. Assume the acceleration due to gravity is equal to
g, and there is no friction between the blocks and the inclined planes. Determine the ratio of
distances traveled by the blocks until both have the same speed.
In an inclined plane AB of 45º to the horizontal, a body is launched in an upward direction rests
for an instant returning to point A. The coefficient of friction between the block and the plane is
\( 2-\sqrt{3\;} \).
Determine the ratio between the interval of time to the body go from A to B and to return
from B to A.
A cart moves over a straight and horizontal surface. In the cart, there is an inclined plane that makes
an angle θ with the horizontal, and on the inclined plane is placed a body. Determine the
acceleration of the cart for the body to remain at rest on the inclined plane. Neglect the friction
between the body and the inclined plane and assume g for the acceleration due to gravity.
A cart moves over a straight and horizontal surface. In the cart there is an inclined plane, it makes an
angle θ with the horizontal plane. On the plane is placed a body, the coefficient of friction
between the body and the plane is μ. Determine the acceleration of the cart, so that the body is
about to rise the plane. Assume g for the acceleration due to gravity.
Atwood Machine
An Atwood machine is arranged in such a way that the masses M1 and
M2 slide without friction over two inclined planes with angles of 30° and 60º
to the horizontal, rather than moving vertically. Assuming that the ropes that support the
masses M1 and M2 are parallel to the planes. Determine:
a) The ratio between M1 and M2 for the system to remain in equilibrium;
b) Calculate the acceleration and tension force on the rope when the masses are equal, each at 5 kg.
Assume the acceleration due to gravity equal to 9.81 m/s2.
a) The ratio between M1 and M2 for the system to remain in equilibrium;
b) Calculate the acceleration and tension force on the rope when the masses are equal, each at 5 kg.
Assume the acceleration due to gravity equal to 9.81 m/s2.
A 12 kg mass body is suspended by a system of pulleys and cords, as shown in the figure, a man pulls the
rope with a force of 18 N. Assuming that the pulleys have no weight and there is no friction between the
pulleys and cords and they are inextensible and massless. Will the body rise or descend? What is
acceleration? The acceleration due to gravity is g = 10 m/s2.
In the system shown in the figure, pulleys 1 and 2 are massless and without friction, pulley 1 is fixed
and pulley 2 is mobile. Block A has a mass of 11 kg and block B rises with an acceleration
of 1 m/s2. Determine the acceleration of block A, the mass of block B, and the
tension force on the rope. Assume the acceleration due to gravity is equal to 10 m/s2.
A rope passes through a fixed pulley in the ceiling, at one end there is a block of
mA = 36 kg, and at the other end a pulley 2. By this second pulley passes a rope in
whose ends are mB = 16 kg and mC = 8 kg (this system is a double
Atwood machine). Calculate the accelerations of the masses and the tension force on the rope. Neglect
the masses and frictions on the pulleys, assuming the acceleration due to gravity is equal to
10 m/s2.
An Atwood machine consists of a block A, with mass equal to 100 kg, and a block B, with
mass equal to 300 kg with the shape of a cube of edge equal to 0.60 m immersed in a container with water.
The blocks are attached by an inextensible rope and negligible mass that passes through a frictionless
pulley and negligible mass. Determine:
a) Acceleration of the system;
b) The tension force on the rope that connects the masses.
Assume the density of water is equal to 1000 kg/m3, and the acceleration due to gravity is equal to 10 m/s2.
a) Acceleration of the system;
b) The tension force on the rope that connects the masses.
Assume the density of water is equal to 1000 kg/m3, and the acceleration due to gravity is equal to 10 m/s2.
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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 .