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Chapter 6: Q.31 (page 155)
A kg locomotive is traveling at when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop? Assume the track is level.
The locomotive roll aboutbefore it stops.
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An object moving in a liquid experiences a linear drag force: , direction opposite to the motion), where is a constant called the drag coefficient. For a sphere of radius the drag constant can be computed as , where is the viscosity of the liquid.
a. Find an algebraic expression for , the -component as a function of time, for a spherical particle of radius and mass that is shot horizontally with initial speed through a liquid of viscosity .
b. Water at has viscosity . Suppose a -diameter, ball is shot horizontally into a tank of water. How long will it take for the horizontal speed to decrease to of its initial value?
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.
It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger鈥檚 weight
a. Before the elevator starts moving?
b. While the elevator is speeding up?
c. After the elevator reaches its cruising speed?
The earth is from the sun. The earth鈥檚 mass is , while the mass of the sun is . What is earth鈥檚 acceleration toward the sun?
The position of a 2.0 kg mass is given by x = 12t 3 - 3t 2 2 m, where t is in seconds. What is the net horizontal force on the mass at
(a) t = 0 s and
(b) t = 1 s?
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