Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. (a) How much work is needed to stretch the spring from 35 cm to 40 cm? (b) How far beyond its natural length will a force of 30 N keep the spring stretched?

Check Your Understanding The spring Example 7.5 is compressed 6 cm from its equilibrium length. (a) Does the spring force do positive or negative work and (b) what is the magnitude?

Two forces act to double the speed of a particle, initially moving with kinetic energy of 1 J. One of the forces does 4 J of work. How much work does the other force do?

Describe a situation in 4iich a force is exerted for a long time but does no work. Explain.

Check Your Understanding What are the values of the gravitational potential energy of the hiker at the base, and sea level, with respect to a sea-level zero of potential energy?

An electron in a television tube is accelerated uniformly from rest to a speed of 8.4107 m/s over a distance of 2.5 cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?

Calculate the power output needed for a 950-kg car to climb a 2.00 slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N.

A particle of mass 2.0 kg moves under the influence of the force F(x)=(5x2=7x)N. If its speed at x=4.0 m is v=20.0 m/s, what is its speed at x=4.0m ?

A particle moving in the xy -plane is subject to a force F(x,y)=(50Nm2)(xi+yj)( x 2 + y 2 )3/2 , where x and y are in meters. Calculate the work done on the particle by this force, as it moves in a straight line from the point (3 in, 4 m) to the point (8 in, 6 in).

A cart is pulled a distance D on a flat, horizontal surface by a constant farce F that acts at an angle with the horizontal direction. The other forces on the object during this time are gravity (Fw) , normal forces (FN1) and (FN2) , and rolling frictions Fr1 and Fr2 , as shown below What is the work done by each force?