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Chapter 6: Q.2 (page 153)
A ball tossed straight up has v = 0 at its highest point. Is it in equilibrium? Explain.
Because of the downward acceleration g, the ball is not in equilibrium at the highest position.
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The piston of a machine exerts a constant force on a ball as it moves horizontally through a distance of . You use a motion detector to measure the speed of five different balls as they come off the piston; the data are shown in the table. Use theory to find two quantities that, when graphed, should give a straight line. Then use the graph to find the size of the piston鈥檚 force.
An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is at . Air resistance is not negligible.
a. Show that the velocity at time t is given by the expression
b. A -wide, -high, car with a drag coefficient of hits a very slick patch of ice while going . If friction is neglected, how long will it take until the car鈥檚 speed drops to ? To ?
c. Assess whether or not it is reasonable to neglect kinetic friction.
The three ropes in are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension in the third rope?
A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is . The ball is pushed to the left, compressing the spring. You鈥檒l learn in Chapter that the spring force on the ball, when the ball is at position (which is negative), can be written as , where k is called the spring constant. The minus sign is needed to make the -component of the force positive. Suppose the ball is initially pushed to , then released and shot to the right.
a. Use what you鈥檝e learned in calculus to prove that
b. Find an expression, in terms of , , and , for the speed of the ball as it comes off the spring at.
If you know all of the forces acting on a moving object, can you tell the direction the object is moving? If yes, explain how. If no, give an example.
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