PHYS 211 Study Guide - Midterm Guide: Point Particle, Weighted Arithmetic Mean, Inertial Frame Of Reference

The kinetic energy of an object of mass moving at a speed is defined as . It seems reasonable to say that the speed of an object--and, therefore, its kinetic energy--can be changed by performing work on the object. In this problem, we will explore the mathematical relationship between the work done on an object and the change in the kinetic energy of that object.

Let us now consider the situation quantitatively. Let the mass of the sled be   and the magnitude of the net force acting on the sled be. The sled starts from rest.

Consider an interval of time during which the sled covers a distance and the speed of the sled increases from  to . We will use this information to find the relationship between the work done by the net force (otherwise known as the network) and the change in the kinetic energy of the sled.

Find the net force  acting on the sled.

Express your answer in terms of someor all of the variables ,,, and .

I)

Find the net work  done on the sled.

Express your answer in terms of someor all of the variables  and .

The kinetic energy of an object of mass moving at a speed is defined as . It seems reasonable to say that the speed of anobject--and, therefore, its kinetic energy--can be changed byperforming work on the object. In this problem, we willexplore the mathematical relationship between the work done on anobject and the change in the kinetic energy of that object.

Let us now consider the situationquantitatively. Let the mass of the sled be  and the magnitude of the net force acting on the sled be. The sled starts from rest.

Consider an interval of time duringwhich the sled covers a distance and the speed of the sled increases from  to . We will use this information to find the relationshipbetween the work done by the net force (otherwise known as thenet work) and the change in the kinetic energy of thesled.

H)

Find the net force  acting on the sled.

Express your answer in terms of someor all of the variables ,,, and .

I)

Find the net work  done on the sled.

Express your answer in terms of someor all of the variables  and .

A block that is being pushed across a frictionless surface by a constant force that is not parallel to the block's velocity. A force (in-network) vs. position (in meter) graph appears below. Note that the graph shows the x-component of the force in blue (i.e., the middle line), the y-component in red (i.e., the bottom line), and the magnitude of the force in green (i.e., the top line). The kinetic energy (in Joules) vs. position (in meters) graph is also plotted for the motion.

1. Choose a distance and describe, in words, how you would use the force vs. position graph to obtain a value for the work done on the block after the block has moved a given distance. Which force did you use? Show your work.

2. What distance did you choose when you determined the work in Q1?

3. Describe, in words, how you would use the kinetic energy vs. position graph to obtain the change in kinetic energy of the block when the block travels the distance that you chose in Q1?

4. How do you answer to Q1 and Q3 compare? What can you conclude?

1. A block is placed on a plane whose angle of inclination is 30˚. The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block
(A) remains stationary on the inclined plane.
(B) accelerates down the inclined plane.
(C) travels down the inclined plane at a constant velocity.
(D) travels up the inclined plane at a constant velocity.
(E) accelerates up the inclined plane.

2. An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30˚ with the horizontal and is 72 m long. The coefficient of friction between the plane and the object is 0.35. The speed of the object at the bottom of the plane is?

3. A 5-kg object slides down a frictionless surface inclined at an angle of 30˚ from the horizontal. The total distance moved by the object along the plane is 10 meters. The work done on the object by the normal force of the surface is?

4. A mass m = 2.5 kg is sliding along a frictionless table with initial speed v as shown in the figure. It strikes a coiled spring that has a force constant k = 500 N/m and
compresses it a distance x=5.0 cm. The initial speed v of the block was..?

5. The graph shows how the position of a particle depends on time. Which choice is closest to the instantaneous speed of the particle at t = 3s?
(A) 0.40 m/s
(B) 0.67 m/s
(C) 0.75 m/s
(D) 1.50 m/s
(E) 2.22 m/s



6. Calculate the work done by a force, F = 2x i, along the
path (0, 0) -> P₁(2, 0) -> P2(2, 2).