A coconut falls out of a tree 12.0 m above the ground and hits a bystander 3.00 m tall on the top of the head. It bounces back up 1.50 m before falling to the ground. If the mass of the coconut is 2.00 kg, calculate the potential energy of the coconut relative to the ground at each of the following sites: (a) while it is still in the tree, (b) when it hits the bystander on the head, (c) when it bounces up to its maximum height.

In the figure, a block of mass m = 4.00 kg slides head on into a spring of spring constant k = 230 N/m. When the block stops, it has compressed the spring by 8.40 cm. The coefficient of kinetic friction between block and floor is 0.480. While the block is in contact with the spring and being brought to rest, what are (a) the work done by the spring force and (b) the increase in thermal energy of the block-floor system? (c) What is the block's speed just as the block reaches the spring? (a) Number -0.81 (b) Number 1.6 (c) Number i -1.1 Units J Units J Units m/s

(a) y = 5.00 m E = F = |m/s² a V = m/s I| || ||||

A 195 g block is pressed against a spring of force constant 1.60 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline (in m) the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block m (b) if the coefficient of kinetic friction is 0.440 m (c) What If? If the ramp is 4.00 m long, what is the maximum coefficient of friction that would allow the block to reach the end of the ramp?

A box of unknown mass is sliding with an initial speed v₁ = 4.30 m/s across a horizontal frictionless warehouse floor when it encounters a rough section of flooring d = 2.80 m long. The coefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring. m/s

A roller-coaster car of mass 1.50 × 103 kg is initially at the top of a rise at point Ⓐ. It then moves 35.0 m at an angle of 50.0° below the horizontal to a lower point Ⓑ. (a) Find both the potential energy of the system when the car is at points Ⓐ and Ⓑ and the change in potential energy as the car moves from point Ⓐ to point Ⓑ, assuming y = 0 at point Ⓑ. (b) Repeat part (a), this time choosing y = 0 at point Ⓒ, which is another 15.0 m down the same slope from point Ⓑ.

A helicopter lifts a 85 kg astronaut 13 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed?

The specialty of an athlete on the women's track team is the pole vault. She has a mass of 60 kg and her approach speed is 8.7 m/s. When she is directly above the bar, her speed is 1.3 m/s. Neglecting air resistance and any energy absorbed by the pole, determine the amount(in m) she has raised herself as she crosses the bar.   Answer in Meters.

A block of mass 3 kg compresses spring 1 with a force constant, k1=7000 N/m, by 6 cm. It is released and slides for a total of 50 cm on a surface with μk=0.2, at which point it compresses another spring 2, k2=1000 N/m, and momentarily comes to rest. Remember that Us is the potential energy of the spring. Find the following values:What is the Initial spring potential energy of spring 1? How much energy is dissipated by heat? This is the amount of work done by friction × -1. How much Potential Energy does spring 2 have when the block has compressed spring 2 and is momentarily stopped? By how much does spring 2 compress?

In the figure, a block of mass m = 3.70 kg slides head on into a spring of spring constant k = 370 N/m. When the block stops, it has compressed the spring by 13.0 cm. The coefficient of kinetic friction between block and floor is 0.300. While the block is in contact with the spring and being brought to rest, what are (a) the work done by the spring force and (b) the increase in thermal energy of the block-floor system? (c) What is the block's speed just as the block reaches the spring?