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Torque

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A force F of magnitude F making an angle theta with the x axis is applied to a particle located along axis of rotation A, at Cartesian coordinates (0, 0) The vector F lies in the xy plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the xy plane.

a). What is the torque (TA) about axis A due to the force F, expressed about axis A at Cartesian coordinates (0, 0).

b). What is the torque (TB) about axis B due to the force F? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y axis.) Express the torque about axis B in terms of F, theta, phi, pi, and/or other given coordinate data.

c). What is the torque (TC) about axis C due to F? (C is the point at Cartesian coordinates (c, 0), a distance c along the x axis.)
Express the torque about axis C in terms of F, theta, phi, pi, and/or other given coordinate data.

d). What is the torque (TD) about axis D due to F? (D is the point located at a distance d from the origin and making an angle phi with the x axis.)

Express the torque about axis D in terms of F, theta, phi, pi, and/or other given coordinate data.

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Torque and Power

Table 1 shows a set of torque-speed measurements for a d.c. electric motor intended for use in an electric wheelchair. Data of this type is used by manufacturers to help specify motor performance.

Table1
Speed /rpm..............600..........1200......1850..........2400.......3050.........3700
Torque /Nm..............5.51..........4.53.......3.75..........2.94........2.09.........1.08

(a) Use the data in Table 1 to plot a suitable graph and obtain the five missing pieces of information, labelled (i)-(v), in the motor specification chart shown in Table 2.

Table 2
.................Stall....................No Load................Maximum Efficiency (Effic)
Operating
Volt /V.......Torque...Current....Speed.....Current...Torque....Speed...Current...Output
................./Nm....... /A.........../rpm ......./A......... /Nm....../rpm....... /A......(Effic)/%

24................(i)........140............(ii)..........5.2.........(iii).......4000.......(iv).........(v)

(b) One of the design requirements for the wheelchair states that the motor must be able to supply 40 Nm of torque at 100 rpm. Determine whether this particular motor has the power to meet that requirement.

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