Uphill Without Slipping A cart of mass M = 46.5 kg is getting ready to carry a crate of mass m= 13.6 kg up a slope of angle #27 with respect to the horizontal, as shown in the figure. The wheels of the cart move freely without friction in their axles and they do not skid over the incline. The coefficients of static and kinetic friction between the crate and the cart are 0.65 and 0.5, respectively. The system is subject to the regular force of gravity (=9.80665 m/s²). The cart is initially at rest while a rope under tension T that is parallel to the slope balances its "down ramp tendency of motion" caused by gravity. At t=0 the magnitude of the tension starts increasing linearly at a rate of 11-5 N/s and the cart accelerates up the slope. (a) Determine the work done by the tension between t= 0 and the moment the crate starts sliding toward the back of the cart. W= 43 (b) Determine the change in the kinetic energy of the crate between t=0 and the moment it starts sliding toward the back of the cart. AK =

Uphill Without Slipping A cart of mass M = 46.5 kg is getting ready to carry a crate of mass m= 13.6 kg up a slope of angle #27 with respect to the horizontal, as shown in the figure. The wheels of the cart move freely without friction in their axles and they do not skid over the incline. The coefficients of static and kinetic friction between the crate and the cart are 0.65 and 0.5, respectively. The system is subject to the regular force of gravity (=9.80665 m/s²). The cart is initially at rest while a rope under tension T that is parallel to the slope balances its "down ramp tendency of motion" caused by gravity. At t=0 the magnitude of the tension starts increasing linearly at a rate of 11-5 N/s and the cart accelerates up the slope. (a) Determine the work done by the tension between t= 0 and the moment the crate starts sliding toward the back of the cart. W= 43 (b) Determine the change in the kinetic energy of the crate between t=0 and the moment it starts sliding toward the back of the cart. AK =

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.24P: A uniform plank is supported by a fixed support at A and a drum at B that rotates clockwise. The...

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Uphill Without Slipping
A cart of mass M = 46.5 kg is getting ready to carry a crate of mass m = 13.6 kg up a slope of angle = 27 with respect to the horizontal, as shown in the figure. The wheels of the cart move freely without friction in their axles and they do not skid over the incline. The
coefficients of static and kinetic friction between the crate and the cart are 0.65 and 0.5, respectively. The system is subject to the regular force of gravity (g = 9.80665 m/s²).
The cart is initially at rest while a rope under tension T that is parallel to the slope balances its "down ramp tendency of motion" caused by gravity. At t=0 the magnitude of the tension starts increasing linearly at a rate of 11.5 N/s and the cart accelerates up the slope.
(a) Determine the work done by the tension between t = 0 and the moment the crate starts sliding toward the back of the cart.
W =
(b) Determine the change in the kinetic energy of the crate between t=0 and the moment it starts sliding toward the back of the cart.
AK=
(c) Determine the magnitude of the acceleration of the crate, with respect to the fixed incline, when it is sliding toward the back of the cart.
m/s²

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Step 2: Find the maximum statics force and time required.

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Step 3: Find the acceleration and distance.

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Step 4: (a)- Determine the work done by the tension force.

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Step 5: b- Find the change in kinetic energy.

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