Question

-A box is pulled up a ramp by a cable at a constant speed There is a friction force between the ramp surface and the box. The work due to friction on the box is?

zero, positive, increasing, negative, or decreasing?

-Consider a pendulum. The magnitude of the masse's velocity is at maximum when?

the mass is at it's lowest point, the mass is at it's highest point, at all points (constant speed), or the initial velocity?

-Consider a rotating disk. The disk has radius R and rotates with angular velocity omega. True or False: All points on the disk share the same angular velocity. But the velocity of points on the disk increases linearly with the distance they are from the rotation axis?

-Suppose we have spring and mass system, i.e. a mass attached to a spring resting on a frictionless horizontal surface. The spring has spring constant k=2 N/m. The mass has mass 1 kg. The spring is set in motion by compressing the spring a distance of 1 cm and then releasing the mass from rest. What is the value for omega, ω. All answers have units of 1/seconds. 2, 2^(1/2), 1, 1/2?

Answer 1

ANSWER 1: Negative. The work due to friction is given by, _Friction =Friction

   .

ANSWER 2:   The velocity is maximum at the Lowest point.  

At the lowest point all the potential energy of the mass of the pendulum is converted into kinetic energy and since Kinetic enery is directly proportional to square of the velocity. So the velocity is maximum at the lowest point.

ANSWER 3: TRUE.

The angular velocity is the total angele moved ( in radian) per second and doesnot depends on the distance from the axis of rotation. So the angular velocity () ,omega is same at all points.

But, the linear velocity ,( v), is dependent on the distance from the axis of rotation by the relation,

.

where r is the distance of the point from the axis of rotation.

ANSWER 4: radian/second.

The angular frequency, () of a horizontal frictionless  mass spring system is given,

where k is the the spring constant, and m is the mass attached to the spring.