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Derive the reduction formula
integeration(x2+a2)n/2dx = x(x2+a2)n/2÷n+1+ na2/n+1×integeration (x2 +a2)n/2-1dx
Use the formula to integrate integration(x2+a2)5/2
A block of ice with mass 1.00kg is initially at rest on a frictionless, horizontal surface. A worker then applies a horizontal force F to it. A a result, the block moves along the x-axis such that its position as a function of time is given by x(t) = 0.100(m/s2) t2 + 0.0100(m/s3) t3. Calculate the work done by the force during the first 1.00s of the motion.
A boy pushes a 9.0kg object a distance of 7.0m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the object and the floor is 0.20. Calculate the work done on the object by the force the boy apply.
Consider five identical beakers. The water level in each beaker is up to the point of overflowing. A toy boat is floating on the surface of beaker A. A second toy boat, one that tipped over and sank to the bottom, is in beaker B. An Ice cube is floating on the surface of beaker C. the block of wood submerged in beaker D is tethered to the bottom by a thread and dab of super glue. (there is nothing in Beaker except water.) The two boats, the ice cube , and the block of wood have equal masses. The density of the submerged boat rests on a scale. Rank the reading on the scales from most to least.
your friend is concerned about a gold ring she bought on a recent trip. The ring was expensive, and she would like to know whether it is really made of gold or of something else. You decide to help her, using your knowledge of physics. You weigh the ring and find that it has a weight of 0.158 N. using a string, you suspend the ring from the scale and, with the ring submerged in water, weight it again to find a new reading of 0.150 N. Is the ring pure gold?
6 m/s x 1.5 kg
Scientists are developing a new space cannon to shoot objects from the surface of the Earth di-
rectly into a low orbit around the Earth. For testing purposes, a projectile is fired with an initial
velocity of 2.8 km/s vertically into the sky.
Calculate the height that the projectile reaches, ...
(a) assuming a constant gravitational deceleration of 9.81 m/s2
.
(b) considering the change of the gravitational force with height.
A marble is thrown horizontally from a tabletop with a velocity of 1.50 m/s. The marble falls 0.70 m away from the table’s edge. How high is the lab table? What is the marble’s velocity just before it hits the floor?
A child of mass 30Kg skates down from the top of a ramp having a constant slope of 15degree. The child's speed increases from 1.5 metre per second to 3.0 metre per second as she reaches the bottom of the ramp. A force of kinetic friction of magnitude 50 Newton opposes her motion draw the appropriate force diagram and determine the length of the ramp take g=10meter per second square
A mass is oscillating with amplitude A at the end of the spring. How far is this mass from the equilibrium if the elastic potential energy equals γ times the kinetic energy?
