Question

A block rests on a frictionless table on Earth. After a 40-N horizontal force is applied to the block, it accelerates at 9.2 m/s2. Then the block and table are carried to the moon, where the acceleration due to gravity is 1.62 m/s2. A horizontal force of 20 N is then applied to the block. What is the acceleration?
5.5 m/s^2
4.1 m/s^2
5.1 m/s^2
4.6 m/s^2
6.0 m/s^2

Answer 1

Answer:

4.6 $\frac{m}{s^2}$

Explanation:

Since the table is frictionless, there is no force of dynamic  friction between table an block when the horizontal force is applied to it on Earth. Exactly the same is true when the table is taken to the Moon. Therefore, the Net Force acting on the object in both cases when the object accelerates, is the external horizontal force.

Notice that on Earth and on the Moon, the weight of the object (vertical and pointing up) is compensated by the normal force of the table on the object (pointing up and of the same magnitude as the weight) that precludes movement in the vertical direction. So in both cases, its acceleration will only be due to the horizontal force.

We use the equation for Net Force to find the mass of the object:

$F=m*a\\40 N =m * 9.2 \frac{m}{s^2}\\\frac{40}{9.2} kg=m\\m=\frac{40}{9.2} kg$

We use this mass (since the mass of the object is a constant independent of where the object is) to find the acceleration the object will experience when the 20 N horizontal force is applied on it on the Moon:

$f=m*a\\20N=\frac{40}{9.2} kg*a\\20*9.2=40*a\\\frac{20*9.2}{40} =a\\a=\frac{9.2}{2} \frac{m}{s^2} \\ a=4.6 \frac{m}{s^2}$