## (solution) 1. A map showing force lines and equal energy contours for a

1. A map showing force lines and equal energy contours for a plane in a conservative field is

shown in Figure 1( in the attachments Figure 1: Conservative Force Field with Energy contours in steps of __ J/kg). The energy contours have units of J/kg. This means the force acting on

an object depends on the mass of the object. Of course, this also means that the amount of

energy transferred to/from the field as an object is moved depends on the mass of the object.

(a) If an object is moved from a position where its center of mass is at point A to a position

where its center of mass is at point B, is energy stored in or retrieved from the field (i.e.

does the mover do positive or negative work on the object in moving it from point A to

point B)?

(b) How much energy is transferred to the field if an object that has a mass of 1 kg is moved

from a position where its center of mass is at point A to a position where its center of

mass is at point B?

(c) How much energy is transferred to the field if a 1 kg object is moved from a position

where its center of mass is at point D to a position where its center of mass is at point A?

(d) Construct a table as shown in Table 1. Determine the amount of energy that the mover

must supply (i.e. the amount of energy transferred to the field) to move a 1 kg mass

between the points listed in Table 1.

(e) A force field is conservative if and only if it takes 0 J of energy to move an object along

any path that ends where it started. Since Figure 1 is a map of a conservative field it

should require a net of 0 J of energy to move a 1 kg object along the path A-B-C-D-E-FG-

A. Verify that this is true using the values in the energy table.

(f) Assume that the distance between neighbouring energy contours in the map of Figure 1 is

1 meter. What is the magnitude of the force exerted by the field on a __ kg mass located

at point A? (Recall that the average force on an object in a force field is the amount of

energy transferred to the object from the field divided by the distance moved in the

direction of the force field.)

(g) What is the magnitude of the force exerted by the field on a __ kg mass located at

point C?

(h) Does the strength of the field depend on the location of the mass?

(i) A 1 kg mass is moved in a straight line from point D to point A. Assume the distance

between energy contours and the distance between force lines are both 1 m.

i. Over what distance is the object moved?

ii. What is the magnitude of the component of the force due to the field that directly

opposes the motion?

iii. Does the work done to move an object from point D to A equal the opposing force

times the distance between points D and A?

iv. What is the magnitude of the component of the force that acts at a right angle to the

direction of movement?

Table 1: Energy table for moving a 1 kg mass

Energy spent by mover

From       to                  to overcome force due to field

A              B

B              C

C              D

D             E

E              F

F             G

G            A

1. A map showing force lines and equal energy contours for a plane in a conservative field is

shown in Figure 1. The energy contours have units of J/kg. This means the force acting on

an object...

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Sep 13, 2020

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