7.–/3 points SerCP9 4.P.063.My Notes
Question Part
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A box rests on the back of a truck. The coefficient of static friction between box and bed of the truck is 0.355.
(a) When the truck accelerates forward, what force accelerates the box?
the inertial force
centripetal force
the friction force
gravity
(b) Find the maximum acceleration the truck can have before the box slides.
m/s2
a) what force is keeping it in place?
b) mu = a/g in this case..
To answer part (a) of the question, we need to understand the different forces acting on the box when the truck accelerates forward. The force that accelerates the box in this case is the friction force.
Explanation to find the force that accelerates the box:
1. In this scenario, the box is at rest, so there is no initial acceleration.
2. When the truck accelerates forward, it applies a force on the box in the same direction.
3. The box's inertia resists this change in motion, wanting to stay at rest.
4. To overcome the inertia, an equal and opposite force needs to be applied to the box.
5. This equal and opposite force is provided by the friction force between the box and the bed of the truck.
Now let's move on to part (b) of the question, where we need to find the maximum acceleration the truck can have before the box slides.
Explanation to find the maximum acceleration:
1. The maximum acceleration occurs when the force of static friction reaches its maximum value.
2. The maximum static friction force can be calculated using the equation: force of static friction (fs) = coefficient of static friction (μs) * normal force (N).
In this case, the normal force is equal to the weight of the box, which is given by the equation: N = mass of the box (m) * acceleration due to gravity (g).
3. Therefore, the maximum static friction force is fs = μs * m * g.
4. To find the maximum acceleration, we equate the maximum static friction force to the mass of the box times its acceleration: m * a = fs.
5. Rearrange the equation to solve for acceleration (a): a = fs / m.
Substituting the value of fs from step 3, we get: a = (μs * m * g) / m.
6. Simplifying the equation, we find that the maximum acceleration is: a = μs * g.
Now, to calculate the maximum acceleration, substitute the given coefficient of static friction (μs) into the equation:
a = (0.355) * (9.8 m/s^2) = 3.479 m/s^2.
Therefore, the maximum acceleration the truck can have before the box slides is approximately 3.479 m/s^2.