A care of mass M 51.5 kg is getting ready to carry a crate of mass m 13.3 kg up a slope of angle 25 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 0.7 and 0.45, 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 J (b) Determine the change in the kinetic energy of the crate between 0 and the moment it starts sliding toward the back of the cart. AK- (e) 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. GN

A care of mass M 51.5 kg is getting ready to carry a crate of mass m 13.3 kg up a slope of angle 25 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 0.7 and 0.45, 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 J (b) Determine the change in the kinetic energy of the crate between 0 and the moment it starts sliding toward the back of the cart. AK- (e) 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. GN

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Uphill Without Slipping
A cart of mass M = 51.5 kg is getting ready to carry a crate of mass m 13.3kg up a slope of angle #25 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 0.7 and 0.45,
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-
4 J
(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
a=

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Step 1: Determine the given data:

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Step 2: Draw the free body diagram:

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Step 3: Determine the initial tension T(0):

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Step 4: Calculation of tension when the crate about to slide to the back of the cart:

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Step 5: Calculate the time measured from t=0 to t=T when the crate starts to slide down:

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Step 6: Calculate the acceleration function of time and equation of displacement:

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Step 7: Calculate the work done by tension force:

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Step 8: Calculate the change in kinetic energy of the crate:

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Step 9: Determine the magnitude of acceleration of the crate when it is sliding towards the back of the cart

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