A certain string can withstand a maximum tension of 40 N without breaking. A child ties a 0.37kg stone to one end and, holding the other end, whirls the stone in a vertical circular radius 0.91 m, slowly increasing the speed until the stone breaks. (a) Where is the stone on its path when the stone breaks? (b) What is the speed of the stone as the string breaks?

Mass (kg) force (n) 5 25 10 50 15 75 20 100 a student was trying to find the relationship between mass and force. he placed four different masses on a table and pulled them using a spring scale. the table shows the different masses used in the experiment and the force required to pull each mass. the student concluded that more force was required to pull heavier objects. what comment would you make regarding his conclusion? a) no clear relation can be observed between mass and force from the data. b) there is a direct proportion between the mass and force listed in the table. c) gravity should have been taken into account while performing the experiment. d) there is an inverse proportion between the mass and force listed in the table.

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.

If a rock is thrown upward on the planet mars with a velocity of 12 m/s, its height (in meters) after t seconds is given by h = 12t − 1.86t2. (a) find the velocity of the rock after two seconds. m/s (b) find the velocity of the rock when t = a. 12−3.72a m/s (c) when will the rock hit the surface? (round your answer to one decimal place.) t = s (d) with what velocity will the rock hit the surface? m/s