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“Gravitational Potential Energy and Kinetic Energy”
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, the projectile stops and explodes into two parts with masses 
and 
. The heavier part of the projectile continues to fly vertically upwards and the lighter part vertically downwards. The total energy at the time of the explosion is 
. Assume that the gravitational acceleration is 
and air resistance is ignored.
after the explosion?
slips from the top of an inclined plane with height 
. The inclined plane extends into a horizontal plane. The horizontal distance between the initial and final position of the body where the body stops is 
(see the figure below). The coefficient of friction between the body and the plane is the same throughout. What is the coefficient of friction between the body and the plane?
and 
are attached to the ends of an unstretchable cord, which is passed over a light pulley. When the heavier body is lifted through a height 
, the lighter body is right on the ground. The friction of the pulley is negligibly small. If the heavier body is dropped from height 
;
does the lighter body rise?
is hung on a 
long light rope. A bullet made of the same substance as the ball is shot with a velocity of 
into the ball. The mass of the bullet is 
and the collision is central and inelastic.
. Before the collision, the projectile and the bullet have the same temperature.
is pushed up a slope inclined at an angle 
to the horizontal at a speed of 
. The coefficient of friction between the slope and the body is 
.
up the slope?
is kept on a smooth slope with height 
which extends into a smooth horizontal plane. When the body is slightly displaced, it begins to slide down the slope and collides with a body of mass 
, which rests at the foot of the slope (see the figure below).
?
at the end of the slope (before the collision)?
is launched at speed 
at an angle 
with respect to horizontal ground. The resistance of the air to the movement of the body is neglected.
travels at a speed of 
uphill with an inclination angle of 
. What is the power of the engine of the car? Friction and air resistance are neglected.
is hung on a 
long string. The body is pulled by hand till it makes an angle 
with the vertical and then pushed at an initial velocity 
in a downward direction, perpendicular to the string. The weight moves in a circular arc, as shown in the figure below. Air resistance is ignored.
is dropped from the top of a curved smooth surface with radius 
. On its way, the cube slides over a belt of rougher horizontal surfaces with length 
. The coefficient of friction between the rough surface and the cube is 
. Then the cube slides over another smooth curved surface on which it stops for a moment and slides back in the opposite direction (see the figure below).
is fired vertically upwards with a gun. At an altitude of 
, the grenade stops and explodes into two parts with masses 
and 
. The heavier part of the grenade continues to fly vertically upwards and the lighter part vertically downwards. The total energy at the time of the explosion is 
. Assume that the gravitational acceleration is 
and air resistance is ignored.
?
rotates along a circle with radius 
on a plane inclined by an angle 
with respect to the horizontal (see the figure below). At point A, the tension in the rope is 
.
. What is the kinetic energy of the body at point B?
hangs a log of mass 
(ballistic pendulum). In the horizontal direction, a ball hits the log at a speed of 
and bounces off the log at a speed of 
. After an elastic collision of the ball with the log, the cord with the log deviates from the vertical by an angle 
.
is thrown at an angle 
with respect to the horizontal (see the figure below). A 
of work is done when the ball is thrown. We assume that the air resistance is negligible.
and the velocity 
of a ball with mass 
, which is dropped to fall freely (see the figure below). Data for the time, height and speed of the ball are collected and recorded in Table 1 below.
, kinetic energy 
and total energy 
of the ball - add additional columns and calculate the values.
. How much electrical energy does the car engine consume?
