A block is on a frictionless table,on earth.The block accelerates at 3.0 m/ $\mathrm { s }^2$ when a $20 \mathrm {~N}$ horizontal force is exerted on it.The block and table are set up on the Moon,where the acceleration of objects due to the gravitational attraction is 1.62 m/ $\mathrm { s }^2$ The weight of the block on the Moon is closest to
A)11 N.
B)9.5 N.
C)8.1 N.
D)6.8 N.
E)5.5 N.

Question

Quizplus · Accepted Answer

The weight of the block on the Moon is equal to the force of gravity acting on it, which is given by:$$W = mg$$where:* $W$ is the weight of the block* $m$ is the mass of the block* $g$ is the acceleration due to gravityOn the Moon, the acceleration due to gravity is 1.62 m/s^2. The mass of the block is not given, but it is the same on Earth and on the Moon. Therefore, the weight of the block on the Moon is:$$W = mg = (1.62 \mathrm{~m/s^2})m$$We do not know the mass of the block, so we cannot calculate the exact weight of the block on the Moon. However, we can compare the weight of the block on the Moon to its weight on Earth. The weight of the block on Earth is:$$W = mg = (9.81 \mathrm{~m/s^2})m$$The ratio of the weight of the block on the Moon to its weight on Earth is:$$\frac{W_{\mathrm{Moon}}}{W_{\mathrm{Earth}}} = \frac{(1.62 \mathrm{~m/s^2})m}{(9.81 \mathrm{~m/s^2})m} = 0.165$$Therefore, the weight of the block on the Moon is 16.5% of its weight on Earth. The closest answer choice to 16.5% is 11 N, which is choice A.

A Block Is on a Frictionless Table,on Earth s2\mathrm { s }^2s2

A Block Is on a Frictionless Table,on Earth $\mathrm { s }^2$