A box rests on the back of a truck. The coefficient of static friction between box and bed of the truck is 0.255.

(a) When the truck accelerates forward, what force accelerates the box?
A)the inertial force
B)gravity
C)centripetal force
D)the friction force

(b) Find the maximum acceleration the truck can have before the box slides.
m/s2

(a) The correct answer is D) the friction force.

When the truck accelerates forward, the box tends to remain at rest due to inertia. However, the static friction force between the box and the bed of the truck opposes this tendency and accelerates the box forward along with the truck. Therefore, it is the friction force that accelerates the box.

(b) To find the maximum acceleration the truck can have before the box slides, we need to consider the maximum static friction force.

The maximum static frictional force (Ffs max) can be calculated using the equation:

Ffs max = µs * N

where µs is the coefficient of static friction and N is the normal force exerted by the truck bed on the box.

The normal force (N) can be calculated as the weight of the box (mg), where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Therefore, the maximum static frictional force is:

Ffs max = µs * mg

To find the maximum acceleration, we equate the maximum static frictional force to the product of box mass (m) and acceleration (a):

µs * mg = m * a

Solving for acceleration (a):

a = µs * g

Substituting the given values, with g approximately equal to 9.8 m/s^2 and the coefficient of static friction (µs) equal to 0.255:

a ≈ 0.255 * 9.8 ≈ 2.509 m/s^2

Therefore, the maximum acceleration the truck can have before the box slides is approximately 2.509 m/s^2.

(a) In order to determine the force that accelerates the box when the truck accelerates forward, we need to consider the forces acting on the box.

There are primarily two forces to consider: the force of gravity pulling the box downward and the force of static friction between the box and the bed of the truck.

- The force of gravity (B) is always acting on the box, regardless of the motion of the truck. It pulls the box downward towards the Earth.
- The force of static friction (D) acts between the box and the bed of the truck and opposes the applied force trying to slide the box. This force prevents the box from sliding when the truck accelerates forward.

Therefore, the correct answer is (D) the friction force.

(b) To find the maximum acceleration the truck can have before the box slides, we can use the equation for static friction:

fs ≤ μs * N

Where:
- fs is the force of static friction
- μs is the coefficient of static friction
- N is the normal force on the box

In this case, the maximum static friction force is required, which occurs just before the box starts to slide. At this point, the force of static friction is at its maximum value and equal to μs * N.

The normal force (N) is equal to the weight of the box, which is mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Therefore, the maximum acceleration the truck can have before the box slides is given by:

μs * N = μs * mg

Substituting the coefficient of static friction (μs) and the values of m and g, you can calculate the maximum acceleration in m/s^2.

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