A single-axle trailer is supported by an axle in the middle of the trailer and a coupler that locks to a ball on the tow vehicle. This ball and socket joint allows for relative motion of the vehicle and trailer while in motion. Care must be used when loading a single axle trailer. The load should be placed in a position that maximizes the force on the axle and minimizes the force on the ball. Upward or downward force on the ball will cause excess wear on the ball and adversely affect the handling of the tow vehicle. A trailer has a mass of mτ = 220 kg. The distance from the coupler to the center of mass of the trailer is r₁ = 1.8 m. The distance from the coupler to the trailer's axle is rA = 2.1 m. Refer to the figure. A Load Otheexpertta.com - Part (a) ✓ Choose the correct free-body diagram for the stationary, unloaded trailer attached to the tow vehicle. Fc denotes the force on the coupler by the ball, and FA denotes the force of the axle. m.g Cheepers.com ✓ Correct! Part (b) Enter an expression for the magnitude of the force exerted on the coupler by the ball, in terms of the defined quantities and g, for the stationary, unloaded trailer. Part (c) Calculate the magnitude of the force exerted on the coupler by the ball, in newtons, for the stationary, unloaded trailer. Part (d) A load of mass m₁ = 510 kg is placed in the back of the stationary trailer at a distance r₁ = 3.15 m from the coupler. Enter an expression, in terms of the defined quantities and g, , for the force exerted on the coupler by the ball, with a positive value representing an upward force. Part (e) Calculate the force (with its sign), in newtons, that the ball exerts on the coupler of the stationary trailer with the load described in part (d): m₁ = 510 kg, r₁ = 3.15 m, and g = 9.81 m/s² Part (f) The same load is now moved to the ideal position that causes the ball to exert zero force on the coupler. Enter an expression, in terms of the defined quantities, for the new distance from the coupler to the load. Part (g) Calculate the new distance from the coupler to the same load, in meters, that results in no force on the coupler: m₁ = 510 kg.
A single-axle trailer is supported by an axle in the middle of the trailer and a coupler that locks to a ball on the tow vehicle. This ball and socket joint allows for relative motion of the vehicle and trailer while in motion. Care must be used when loading a single axle trailer. The load should be placed in a position that maximizes the force on the axle and minimizes the force on the ball. Upward or downward force on the ball will cause excess wear on the ball and adversely affect the handling of the tow vehicle. A trailer has a mass of mτ = 220 kg. The distance from the coupler to the center of mass of the trailer is r₁ = 1.8 m. The distance from the coupler to the trailer's axle is rA = 2.1 m. Refer to the figure. A Load Otheexpertta.com - Part (a) ✓ Choose the correct free-body diagram for the stationary, unloaded trailer attached to the tow vehicle. Fc denotes the force on the coupler by the ball, and FA denotes the force of the axle. m.g Cheepers.com ✓ Correct! Part (b) Enter an expression for the magnitude of the force exerted on the coupler by the ball, in terms of the defined quantities and g, for the stationary, unloaded trailer. Part (c) Calculate the magnitude of the force exerted on the coupler by the ball, in newtons, for the stationary, unloaded trailer. Part (d) A load of mass m₁ = 510 kg is placed in the back of the stationary trailer at a distance r₁ = 3.15 m from the coupler. Enter an expression, in terms of the defined quantities and g, , for the force exerted on the coupler by the ball, with a positive value representing an upward force. Part (e) Calculate the force (with its sign), in newtons, that the ball exerts on the coupler of the stationary trailer with the load described in part (d): m₁ = 510 kg, r₁ = 3.15 m, and g = 9.81 m/s² Part (f) The same load is now moved to the ideal position that causes the ball to exert zero force on the coupler. Enter an expression, in terms of the defined quantities, for the new distance from the coupler to the load. Part (g) Calculate the new distance from the coupler to the same load, in meters, that results in no force on the coupler: m₁ = 510 kg.
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A single-axle trailer is supported by an axle in the middle of the trailer and a coupler that locks to a ball on the tow vehicle. This ball and socket joint allows for relative motion of the vehicle and trailer while in motion. Care must be used when loading a single axle trailer. The load should be placed in a position that maximizes the force on the axle and minimizes the force on the ball. Upward or downward force on the ball will cause excess wear on the ball and adversely affect the handling of the tow vehicle. A trailer has a mass of mT = 220 kg. The distance from the coupler to the center of mass of the trailer is rT = 1.8 m. The distance from the coupler to the trailer’s axle is rA = 2.1 m. Refer to the figure.
Transcribed Image Text:A single-axle trailer is supported by an axle in the middle of the trailer and a coupler that locks to a ball on
the tow vehicle. This ball and socket joint allows for relative motion of the vehicle and trailer while in motion.
Care must be used when loading a single axle trailer. The load should be placed in a position that maximizes
the force on the axle and minimizes the force on the ball. Upward or downward force on the ball will cause
excess wear on the ball and adversely affect the handling of the tow vehicle. A trailer has a mass of mτ = 220
kg. The distance from the coupler to the center of mass of the trailer is r₁ = 1.8 m. The distance from the
coupler to the trailer's axle is rA = 2.1 m. Refer to the figure.
A
Load
Otheexpertta.com
- Part (a) ✓
Choose the correct free-body diagram for the stationary, unloaded trailer attached to the tow vehicle. Fc denotes the force on the coupler by the ball, and FA denotes
the force of the axle.
m.g
Cheepers.com
✓ Correct!
Part (b)
Enter an expression for the magnitude of the force exerted on the coupler by the ball, in terms of the defined quantities and g, for the stationary, unloaded trailer.
Part (c)
Calculate the magnitude of the force exerted on the coupler by the ball, in newtons, for the stationary, unloaded trailer.
Part (d)
A load of mass m₁ = 510 kg is placed in the back of the stationary trailer at a distance r₁ = 3.15 m from the coupler. Enter an expression, in terms of the defined
quantities and g, , for the force exerted on the coupler by the ball, with a positive value representing an upward force.
Part (e)
Calculate the force (with its sign), in newtons, that the ball exerts on the coupler of the stationary trailer with the load described in part (d): m₁ = 510 kg, r₁ = 3.15 m,
and
g = 9.81 m/s²
Part (f)
The same load is now moved to the ideal position that causes the ball to exert zero force on the coupler. Enter an expression, in terms of the defined quantities, for the
new distance from the coupler to the load.
Part (g)
Calculate the new distance from the coupler to the same load, in meters, that results in no force on the coupler: m₁ = 510 kg.
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