Exam 6: Potential Energy and Energy Conservation

Block A is dropped from a height of 2 m.A second identical block B slides frictionlessly down a ramp of height 2 m inclined at 30 ^$\circ$ .A third identical block C slides down a frictionless ramp of height 2 m inclined at 45 ^$\circ$ .Which block is travelling fastest at the bottom of the ramp?

Find the magnitude of the force at the position x = 2.0 m and y = 3.0 m associated with the potential energy function U = (7.0 J)+ (5.0 J/m)x + (4.0 J/m)y.

A stone is thrown up in the air and it reaches a maximum height of 10.0 m.What is the initial speed of the stone?

A 30.0-kg child slides down a long slide in a play- ground.She starts from rest at a height h₁ of 22.00 m.When she is partway down the slide,at a height h₂ of 13.00 m,she is moving at a speed of 9.10 m/s.Calculate the mechanical energy lost due to friction (as heat,etc.).(in J)

541 J of work is required to slide a 20-kg ice block up a frictionless slope.The incline of the slope with respect to horizontal is 9.71 ^$\circ$ .What is the length of the slope?

A steel ball of mass 0.5 kg is fired vertically up from the edge of a building 20 m high with an initial speed of 10 m/s.When it falls back on the ground at the base of the building,it gets buried in sand to a depth of 0.2 m.Determine: the average resistance force that sand exerts on the ball.

Calculate the gravitational potential energy relative to the ground of a 35.0-kg rock is 1.75 m above the ground.

An 80-kg fireman slides down a 3-meter pole by applying a frictional force against the pole using his hands.If he slides from rest and he land on the ground with a speed of 6.00 m/s,the frictional force his hands applied against the pole was

How much mechanical energy is lost to friction if a 22-kg box slides 7.0 m down a rough inclined plane at a constant speed of 11 m/s? The inclined plane makes an angle of 33 degrees with respect to the horizontal.

Find the y-component of the force at the position x = 2.0 m and y = 3.0 m associated with the potential energy function U = (7.0 J)+ (5.0 J/m)x + (4.0 J/m)y.

The turning points for a 0.25-kg object in a potential of are $\pm$ 0.50 m .What is the maximum kinetic energy of the object in this potential?

A person standing on top of a 40-m high cliff throws a rock with a mass of 0.25 kg off the cliff.The rock leaves the person's hand with a speed of 14 m/s and makes an angle of 60 degrees above the horizontal.What is the kinetic of the rock when it reaches the top of its path?

A spring,with k = 2500N/m,is fixed vertically to the floor.A 10.0-kg box is then pressed down such that the spring is compressed 0.5 m beyond its equilibrium length.The box is then released and the box travels vertically upward reaching a maximum height of 2.24 m above its release point.What is the work done by the resistive forces (drag/air resistance)?

A loaded wheelbarrow with a total mass of 70 kg is moved from the bottom to the top of a 2.5-m tall hill.The change in the potential energy of the loaded wheelbarrow is

Find the PE of a 25-kg object 1.67 m above the surface of the National Mall in Washington,DC.Take the surface of Tiananmen Square to be zero potential.Possibly useful information Beijing elevation: 43 m above sea level. National Mall elevation: 10 m above sea level Radius of the Earth: 6.38 * 10⁶ m. Assume that DC and Beijing are directly opposite each other for this problem.

In figure,the 2-kg mass has an initial velocity of 1 m/s down the ramp when it is 3 m up from the tip of a spring along a 30-degree ramp.The coefficient of kinetic friction between the ramp and the mass is 0.2.The spring at the bottom of the ramp is 200 cm long.The maximum compression the spring when the mass collides with it is 0.5 m.What is the spring constant of the spring?

A 5.0-kg pumpkin is dropped from the top of the RCA Building in New York City.If it falls through a distance of 380 m,and splats on the sidewalk with a speed of 52.0 m/s,what is the work done by air resistance during its fall?

The potential energy of a 10-kg mass is given by -3.98 * 10¹⁵ r^-1 (potential energy decreases as r approaches zero).The force on this mass when it is located at r=6.38 * 10⁶ m is

The potential energy of an object as a function of position is U(x)= x³ + 8,where U is measured in joules and x is measured in meters.Where is the object be located if it is in a metastable equilibrium?

Find the x-component of the force at the position x = 2.0 m and y = 3.0 m associated with the potential energy function U = (7.0 J)+ (5.0 J/m)x + (4.0 J/m)y.