Answer to Question #244417 in Physics for Kimberly

Question

A) A shopping trolley and its contents have a total mass of 42kg. the trolley is being pushed along a horizontal surface at a speed of 1.2ms−1 . When the trolley is released, it travels a distance of 1.9m before coming to rest. A ssuming that the total force opposing the motion of the trolley is constant.

(i) Calculate the deceleration of the trolley.

(ii) Show that the total force opposing the motion of the trolley is 16N

(iii) Using the answer in A (ii), calculate the power required to overcome the total force opposing the motion of the trolley at a speed of 1.2msm−1 .

B) A stone falls from rest, calculate the distances through which it has fallen at times 1, 2, 3, 4 seconds after being released. Show that the distances travelled during the 1 𝑠𝑡 , 2 𝑛𝑑 , 3 𝑟𝑑 and 4 𝑡ℎ second after being released are in the ratio 1: 3: 5: 7. Find the formula for the distance fallen in the 𝑛 𝑡ℎ second.

Answer 1

A) (i) The deceleration:

$$a=\frac{v^2}{2d}=0.38\text{ m/s}^2.$$

(ii) The force is

$$F=ma=42·0.38=16\text{ N}.$$

(iii) The power is

$$P=Fv=16·1.2=19.2\text{ W}.$$

B) 1 second:

$$d_1=\frac{gt_1^2}{2}=\frac g2.$$

Another seconds:

$$d_2=\frac{gt_2^2}{2}-d_1=1.5g.\\\space\\ d_3=\frac{gt_3^2}{2}-\frac{gt_2^2}{2}=2.5g.\\\space\\ d_4=\frac{gt_4^2}{2}-\frac{gt_3^2}{2}=3.5g.$$

Multiplied by 2, all values of d above become 1g:3g:5g:7g, or 1:3:5:7.