Oh.
F(along radius) = ma
μmg=mv²/r
μg=v²/r
μgr=v²
v²=(0.550)(9.80)(37.9)
v ~= 14.3m/s
F(along radius) = ma
μmg=mv²/r
μg=v²/r
μgr=v²
v²=(0.550)(9.80)(37.9)
v ~= 14.3m/s
Since the crate is located in the middle of the flat bed of the truck, it experiences a centripetal force towards the center of the circular path. This force is provided by the frictional force between the crate and the truck bed.
The maximum frictional force between two surfaces can be found using the equation:
F_friction = coefficient of static friction * normal force
where the normal force is the force exerted by the truck bed on the crate, which is equal to the weight of the crate (mass * gravity).
Since the crate is not sliding, the maximum frictional force must be equal to the centripetal force:
F_friction = centripetal force
The centripetal force can be calculated as:
F_centripetal = mass * (velocity^2 / radius)
In this case, the radius is given as 37.9 m.
Combining the equations, we have:
coefficient of static friction * (mass * gravity) = mass * (velocity^2 / radius)
The mass cancels out from both sides, so we have:
coefficient of static friction * gravity = velocity^2 / radius
Now, we can rearrange the equation to solve for velocity:
velocity^2 = coefficient of static friction * gravity * radius
velocity = sqrt(coefficient of static friction * gravity * radius)
Plugging in the given values:
coefficient of static friction = 0.550
radius = 37.9 m
gravity = 9.8 m/s^2
velocity = sqrt(0.550 * 9.8 * 37.9)
Calculate the square root and we get the final answer:
velocity ≈ 21.69 m/s
Therefore, the truck can move at a maximum speed of approximately 21.69 m/s without the crate sliding.