0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a $$10 000kg$$ load sits on the flatbed of a $$20 000kg$$ truck moving at $$12.0 m/s$$. Assume that the load is not tied down to the truck, but has a coefficient of friction of $$0.500$$ with the flatbed of the truck. (a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck. (b) Is any piece of data unnecessary for the solution.

Solution
Verified by Toppr

If the load is on the point of sliding forward on the bed of the slowing truck, static friction acts backward on the load with its maximum value, to give it the same acceleration as the truck:
$$\sum F_{x} = ma_{x} : − f_{s} = m_{load}a_{x}$$
$$\sum F_{y} = ma_{y} : n − m_{load}g = 0$$
Solving for the normal force and substituting into the $$x$$ equation gives:
$$-\mu_{s}m_{load}g = m_{load}a_{x}$$ or $$a_{x} = −\mu_{s}g$$
We can then use
$$v_{xf}^{2}=v_{xi}^{2}+2a_{x}(x_{f}-x_{i})$$
Which becomes
$$0=v_{xi}^{2}+2(-\mu_{s}g)(x_{f}-0)$$
(a) $$x_{f}=\frac{v_{xi}^{2}}{2\mu_{s}g}=\frac{(12.0m/s)^{2}}{2(0.500)(9.80m/s^{2})}=14.7m$$
(b) From expression $$x_{f}=\frac{v_{xi}^{2}}{2\mu_{s}g}$$
neither mass affects the answer.

Was this answer helpful?
2
Similar Questions
Q1
Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a $$10 000kg$$ load sits on the flatbed of a $$20 000kg$$ truck moving at $$12.0 m/s$$. Assume that the load is not tied down to the truck, but has a coefficient of friction of $$0.500$$ with the flatbed of the truck. (a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck. (b) Is any piece of data unnecessary for the solution.
View Solution
Q2
Consider a large truck carrying a heavy load, such as steam beam. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 10000 kg load is located on the flatbed of a truck moving at 12.0 m/s. Assume the load is not tied down to the truck and assume that the coefficient of friction between the load and truck bed is 0.500. Calculate the minimum stopping distance for the truck, at which the load will not slide forward relative to the truck.
View Solution
Q3
A large crate of mass $$m$$ is place on the flatbed of a truck but not tied down. As the truck accelerates forward with acceleration $$a$$, the crate remains at rest relative to the truck. What force causes the crate to accelerate?
View Solution
Q4
The driver of a speeding empty truck slams on the brakes and skids to a stop through a distance d. On a second trial, the truck carries a load that doubles its mass. What will now be the trucks skidding distance"?
View Solution
Q5
An empty truck moving on a straight road with a certain velocity can be stopped over a distance s by applying the brakes. If the truck is loaded so that its mass now is one and half times that of the empty truck and is moving with the same velocity, it can be stopped by the brakes in a distance of (assume that the same braking force is acting in the two cases)
View Solution