Mechanics | Relativity Answers

Consider the conservation of energy equation below.
ΔK + ΔU + ΔEint = W + Q + TMW + TMT + TET + TER
A ball of mass m falls from a height h to the floor.
(a) Identify the appropriate version of the equation above for the system of the ball and the Earth.
ΔEint = Q +TET + TER
or
ΔU = W
or
ΔK + ΔU = 0
or
ΔK = W
Use this equation to calculate the speed of the ball just before it strikes the Earth. (Use the following as necessary: m for mass, h for height, g for acceleration due to gravity.)
v =

(b) Identify the appropriate version of the equation above for the system of the ball.
ΔK = W
or
ΔEint = Q +TET + TER
or
ΔU = W
or
ΔK + ΔU = 0
Use this equation to calculate the speed of the ball just before it strikes the Earth. (Use the following as necessary: m for mass, h for height, g for acceleration due to gravity.)

A bead with a hole through it slides on a wire track. The wire is threaded through the hole in the bead, and the bead slides without friction around a loop-the-loop (see figure below). The bead is released from rest at a height
h = 3.00R.
a. What is its speed at point A? (Use the following as necessary: the acceleration due to gravity g, and R.)
b. How large is the normal force on the bead at point A if its mass is 4.90 grams? magnitude and direction?
c. What If? What is the minimum height h from which the bead can be released if it is to make it around the loop? (Use any variable or symbol stated above as necessary.)

As shown in the figure, a 0.540 kg container is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The force constant of the spring is 450 N/m. When it is released, the container travels along a frictionless, horizontal surface to point A, the bottom of a vertical circular track of radius
R = 1.00 m,
and continues to move up the track. The speed of the container at the bottom of the track is vA = 12.3 m/s, and the container experiences an average frictional force of 7.00 N while sliding up the track.
a. What is x?
b. If the container were to reach the top of the track, what would be its speed (in m/s) at that point?
c. Does the container actually reach the top of the track, or does it fall off before reaching the top?
reaches the top of the track or falls off before reaching the top or not enough information to tell

A 5.80–kg block is set into motion up an inclined plane with an initial speed of vi = 8.20 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of θ = 30.0° to the horizontal.
(a) For this motion, determine the change in the block's kinetic energy.
(b) For this motion, determine the change in potential energy of the block–Earth system.
(c) Determine the friction force exerted on the block (assumed to be constant).
(d) What is the coefficient of kinetic friction?

For saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 12.0 mi/h, a cyclist uses food energy at a rate of about 420 kcal/h above what he would use if merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here 1 kcal = 1 nutritionist's Calorie = 4186 J.) Walking at 2.80 mi/h requires about 210 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about 1.30 x10^8 J/gal.
(a) Find the fuel economy in equivalent miles per gallon for a person walking.
(b) Find the fuel economy in equivalent miles per gallon for a person bicycling.

A crate of mass 9.6 kg is pulled up a rough incline with an initial speed of 1.44 m/s. The pulling force is 104 N parallel to the incline, which makes an angle of 20.3° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.02 m.
(a) How much work is done by the gravitational force on the crate?
(b) Determine the increase in internal energy of the crate–incline system owing to friction.
(c) How much work is done by the 104-N force on the crate?
(d) What is the change in kinetic energy of the crate?
(e) What is the speed of the crate after being pulled 5.02 m?

A 0.18-kg stone is held 1.1 m above the top edge of a water well and then dropped into it. The well has a depth of 4.7 m.
(a) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system before the stone is released?
(b) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system when it reaches the bottom of the well?
(c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?

a 0.0585 kg tennis ball is twirled at the end of a thread in a horizontal circle with radius of 0.75m with a height of 2m above the ground. the thread breaks and the balls travels a horizontal distance of 18.4 m before bouncing off the ground. what is the tension on the thread before it snapped?

a car is traveling on a road that passed through rolling terrain. at the bottom of one particular dip in the road which may be approximately as a vertical circle of radius 65m, the car and driver are moving with an instantaneous horizontal velocity of 17m/s. if the mass of the driver is 80kg what is the apparent weight of the driver at the bottom of the dip

In kinetics,when one block is placed on top of another is a pulley system,if one accelerate to the left,they get a negative acceleration while the one accelerating to the right gets positive acceleration.So negative sign not only means slowing down but also accelerate in opposite direction?