It is required to design a tennis ball for recreational use by settlers on Mars. The primary requirement is that the balls must pass the same 'bounce test' specified for tennis balls used on Earth. This requires that a ball dropped from a height of 254 cm onto concrete will bounce back to a height of 140 cm. The games will be played in a sealed gymnasium pressurised with standard air to 70 kPa. The balls are to have the same mass and diameter as those used on Earth, with modifications to account for the reduced gravity on Mars and the lower air pressure in the habitat. The height a ball recovers after a single bounce is believed to depend on the following parameters: Earth Drop height, L (m) Gravitational acceleration, g (m/s²) Internal pressure of ball above atmospheric (kPa) Diameter, D (m) Mass of ball, M (kg) Target bounce height, h (m) 2.54 9.8 83 0.067 0.057 0.14 Mars 2.54 3.71 ? 0.067 0.057 0.14 0 ms 2 ms 4 ms 3 ms a) Identify the dimensionless parameters which would control the bounce height under these assumptions. b) What pressure should the balls be filled to?

2. Calculate the mass of silver initially at 445 °C which would be needed to be dropped into a 435 mL sample of water initially at 23.0 °C in an insulated container to raise the temperature of the water to 33.5 °C. The specific heat capacity of water is 4.184 J K-¹ g¹ and the molar heat capacity of silver is 25.9 J K¹ mol¹¹. 2 Tot 21

Q22. An object is shot straight up from 7 m above ground level, and returns to the ground after 2.3 s. If the effects of the air are neglected, what is the highest position it has reached (as measured from the ground)? Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper SI unit. Take g = 9.81 m/s². Your Answer: Answer units

Thermodynamics Question! Please and thank you for all your help! Please make sure the answer is valid and in the correct units!

Q3. In the image shown below, according to the provided datum line, determine the gravitational potential energy of the 5.9-kg block. The radius r = 2.6 m and the angle 0 = 29°. Negative sign must be included if the energy is negative. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper SI unit. Take g = 9.81 m/s². Your Answer: Answer Ө units Datum

A boxer delivers a hard blow to the chin of his opponent. The inertia of the boxer's hand (with glove) and forearm is 3.0 kg, and the inertia of the opponent's head is 6.5 kg. You learned in neurobiology class about 10 J of extra internal energy will render an opponent wobbly - kneed, and you guess that about half of the converted energy will end up in the opponent's head. Assuming a coefficient of restitution e = 0.20, with what speed does the boxer's fist have to contact the opponent's head in order to deliver the punch?

Problem Description You are stuck in an elevator with a meter stick, a spring with a spring constant of 30 N/m, and an object with a mass of exactly 0.5 kg. When you suspend the object from the end of the spring, you find that the spring stretches by 18 cm. Determine everything you can about the motion of the elevator from this information. Instructions In a neat and organized fashion, write out a solution which includes the following: 1. A sketch of the physical situation with all given physical quantities clearly labeled. 2. Represent the forces exerted on the object using a force diagram and, after you have made your determinations about the motion of the elevator, construct possible motion diagrams representing the motion of the elevator (if you think there is only one possible motion draw that, if you think there are several possible motions draw motion diagrams for each of them). 3. Determine everything you can about the motion of the elevator. Use your force diagram and…