Answer to Question #112415 in Mechanics | Relativity for Jess

Question

A truck with a 1000kg load sitting on its flat deck is driving round a circle of radius 100m on a flat, horizontal road at a steady speed of 10ms-1 (36kmhr-1). The load is not secured, but is not sliding on the flat deck of the truck. Which ONE of the following statements is FALSE?

(a) The magnitude of the acceleration of the load is 1ms-2
(b) The upward normal force on the load is 10000N
(c) The total vertical force on the load is zero
(d)The total horizontal force on the load is zero
(e) The magnitude of the frictional force on the load is approximately 1000N

Answer 1

Calculations & Explanations

a)

• The lorry along with the load moves at a constant speed so that, there isn't a tangential acceleration. As common for every circular motion, only the centripetal acceleration applies.
• Therefore,

$\qquad\qquad \begin{aligned} \small a&= \small \frac{v^2}{r}\\ \small &= \small \frac{100m^2s^{-2}}{100m}\\ \small &= \small \bold{1ms^{-2}}\cdots\cdots(\text{statement is correct}) \end{aligned}$

b) & c)

• The upward normal force is the resultant force acts on the load from the lorry deck. And it equals the weight of it (R = mg=10000N), since the load is at rest on the lorry deck.
• Resultant force & the weight of the load are the only vertical forces acts on it. As it is at rest on the deck we see that there is no any vertical acceleration. Zero acceleration along a given direction implies zero net force along that direction. So the net vertical force is zero.
• So both the statements are correct.

e)

• Since the frictional force provides the centripetal force needed for the circular motion it can be calculated,

$\qquad\qquad \begin{aligned} \small F&= \small ma_{centripetal}\\ \small &= \small 1000kg \times1ms^{-2}\\ \small&= \small \bold{1000N}\cdots\cdots(\text{statement is correct}) \end{aligned}$

d)

• For a circular motion to be possible there should be a centripetal force.
• So the total horizontal force should be non-zero.
• Here, the sole horizontal force is the frictional force from the deck.
• Even the circular motion takes place with a centripetal acceleration of 1ms^-2
• Therefore, total horizontal force is not zero. (incorrect statement)