Download Chapter 6 HW 2

Chapter 6 – Work and Energy
HW 2
1.
A 3.0—kg object moving along the x
axis has a velocity of 2.4 m/s as it
passes through the origin. It is acted
on by a single force, Fx, that varies
with x, as shown in Figure 6-31. (a)
Find the work done by the force
from x = 0.0 m to x = 2.0 m. (b)
What is the kinetic energy of the
object at x = 2.0 m? (c) What is the
speed of the object at x = 2.0 m? (d)
What is the work done on the object
from x = 0.0 to x = 4.0 m. (e) What
is the speed of the object at x = 4.0
m?
2.
A 6.0—kg block slides 1.5 m down a frictionless incline that makes an angle of 60° with the horizontal. (a)
Draw the free-body diagram of the block, and find the work done by each force when the block slides 1.5 m
(measured along the incline). (b) What is the total work done on the block? (c) What is the speed of the block
after it has slid 1.5 m, if it starts from rest? (d) What is its speed after 1.5 m, if it starts with an initial speed of
2.0 m/s?
Chapter 6 – Work and Energy
HW 2
3.
Particle a has mass m, is initially located on the positive x axis at x = x0 and is subject to a repulsive force Fx
from particle b. The location of particle b is fixed at the origin. The force Fx is inversely proportional to the
2
square of the distance x between the particles. That is, F x = A/x , where A is a positive constant. Particle a is
released from rest and allowed to move under the influence of the force. Find an expression for the work
done by the force on a as a function of x. Find both the kinetic energy and speed of a as x approaches infinity.
4.
A single horizontal force in the +x direction acts on a cart of mass m. The cart starts from rest at x = 0, and
the speed of the cart increases with x as
, where C is a constant. (a) Find the force acting on the
cart as a function of x. (b) Find the work done by the force in moving the cart from x = 0 to x = x1.
Chapter 6 – Work and Energy
HW 2
5.
A box of mass M is at rest at the bottom of a frictionless inclined plane (Figure 6-38). The box is attached to
a string that pulls with a constant tension T. (a) Find the work done by the tension T as the box moves
through a distance x along the plane. (b) Find the speed of the box as a function of x. (c) Determine the power
delivered by the tension in the string as a function of x.