A string 1.0 m long breaks when its tension is 100 N. What is the greatest speed at which it can be used to whirl a 1.0 kg stone? (Neglect the gravitational pull of the earth on the stone.)

A child is standing on the edge of a cliff overlooking a river. The cliff is 8 m above the edge of the river and the river is 20 m wide where the child is located. If the child can throw a rock with a speed of 20 m/s, will the rock make it across the river?

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An Atwood's machine consists of two masses m₁ and m₂ joined by a light cord which passes over a pulley. Initially, the heavier mass is positioned a distance h above the floor. The masses are released from rest. At what speed are the masses moving when the heavier mass strikes the floor? Here m₁ = 4kg, m₂ = 6kg, and h = 3m. The cord is long enough so that the lighter mass does not reach the pulley. Devices like this are used in the construction of elevators. (3.4 m/s)

Before they were decommissioned, the NASA space shuttles required two solid rocket boosters (SRBs) to launch the shuttle from Earth’s surface. Both SRBs produced 1.7 x10^7 N at liftoff. The combined mass of a shuttle and rocket boosters was about 1.5 x 10^6 kg. (5 marks) (a) Calculate the net acceleration of a space shuttle and rockets at the time of liftoff. (b) Calculate the speed of the shuttle and rockets after 10.0 s

In the problems below, “little g” plays a variety of roles. Near the earth’s surface, g has a value of 9.81 m/s2. At other locations g may have different values. Solve these word problems using the data provided below. MMoon = 7.35 × 1022 kg rMoon  = 1.74 × 106 m rMoon’s orbit = 3.8 x 108 m mEarth = 5.97 × 1024 kg rEarth  = 6.37 × 106 m rEarth’s orbit = 1.5 x 1011 m Question 1: An astronaut is standing on the moon, holding a feather. a) Calculate the acceleration due to gravity on the moon. b) The astronaut drops the feather from a height of 2.0 meters. How long does it take the feather to hit the ground? c) The feather has a weight of 0.020 N on Earth. What is its weight on the moon?

Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 8.8 kgkg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at 3.7 m/s . What upward force must a branch provide to support the swinging gibbon?

Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

A 1,865.66 kg car at rest at the top of a hill 20 m high is given a nudge and begins to roll down the hill.  It rolls up a 8.39 m hill on the other side.  How fast is it moving as it tops the lower hill?

A commercial jet is coming in for landing. Just before it hits the runway it is moving 76m/s. Plane has a mass of 20,000kg. The runway is 1.6km long and the plane needs to stop before the end of the runway. How large is the braking force the airplane needs to stop safely?