5.36 The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s-2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).
From the equation F = ma, we get the backward acceleration produced in the box
a = 20/40 = 0.5 m/s2
From the equation s = ut + , to travel s = 5 m by the box to fall off from the truck, we get
5 = 0 + 0.5
5 = 0.25 , t = 4.47 s
The travel of truck during t = 4.47 s is
= 0 + 0.5 = 0.5 = 19.98 m
<p>Force on the box, F = MA = 40 <span title="Click to copy mathml"><math><mo>*</mo></math></span> 2 N = 80 N</p><p>Frictional force, Ff = <span title="Click to copy mathml"><math><mi>? </mi><mi>m</mi><mi>g</mi></math></span> = 0.15 <span title="Click to copy mathml"><math><mo>*</mo><mn>40</mn><mi></mi><mo>*</mo><mn>10</mn><mo>=</mo></math></span> 60 N</p><p>Net force = F – Ff = 80 – 60 = 20 N</p><p>From the equation F = ma, we get the backward acceleration produced in the box</p><p>a = 20/40 = 0.5 m/s2</p><p>From the equation s = ut + <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mi>a</mi><msup><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span> , to travel s = 5 m by the box to fall off from the truck, we get</p><p>5 = 0 <span title="Click to copy mathml"><math><mo>*</mo><mi>t</mi></math></span> + <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></span> <span title="Click to copy mathml"><math><mo>*</mo></math></span> 0.5 <span title="Click to copy mathml"><math><mo>*</mo><mi></mi><msup><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span></p><p>5 = 0.25 <span title="Click to copy mathml"><math><msup><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span> , t = 4.47 s</p><p>The travel of truck during t = 4.47 s is</p><p>= 0 <span title="Click to copy mathml"><math><mo>*</mo><mi>t</mi></math></span> + <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></span> <span title="Click to copy mathml"><math><mo>*</mo></math></span> 0.5 <span title="Click to copy mathml"><math><mo>*</mo><mi></mi><msup><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span> = 0.5 <span title="Click to copy mathml"><math><mo>*</mo><mn>2</mn><mi></mi><mo>*</mo><msup><mrow><mrow><mn>4.47</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span> = 19.98 m</p>
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