A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide? a. 14 m b. 11 m c. 19 m d. 24 m e. 29 m
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to use the following equation that relates the distance, speed, acceleration and time such that:
`d = v_0*t + (at^2)/2`
Since the car starts from rest, the initial speed is `v_0 = 0` and the time of 3 s is provided by the problem, hence, substituting these values in equation above yields:
`d = 9a/2`
You need to find the value of acceleration, hence, using the Newton's second law of motion yields:
`m*a = F_f`
`F_f ` represents the friction force
`F_f = mu*N = mu*m*g => m*a = mu*m*g => a = mu*g`
Since the problem provides the coefficient of static friction mu = 0.24 and considering `g = 9.8 m/s^2` yields:
`a = 0.24*9.8 = 2.352 m/s^2`
Substituting `2.352 ` for a in equation`d = 9a/2` yields:
`d = 9a/2 => d = 9*2.352/2 = 10.584 m` ~~ 11m
Hence, evaluating the maximum distance the truck can travel, without having the box slide, yields `d~~11 m` , thus, you may select the answer b.
Related Questions
- A 150 N box is being pulled horizontally in a wagon accelerating uniformly at 3.00 m/s2. The...
- 1 Educator Answer
- What is the tension in the rope that connects the boxes? What is the mass m of the second box?...
- 1 Educator Answer
- A 75 pound box rests on a perfectly smooth horizontal surface. Any horizontal force greater than...
- 1 Educator Answer
- A driver in a 1000.0 kg car traveling at 20 m/s slams on the brakes and skids to a stop. If the...
- 1 Educator Answer
- A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The...
- 1 Educator Answer