Question

An object of mass 3 kg is moving on a rough surface with a velocity of 16m/s .It covers a distance of a of 20m before coming to rest.find the the opposing force.

Answer 1

Answer on Question#39127 – Physics – Mechanics | Kinematics | Dynamics

An object of mass $3\,\mathrm{kg}$ is moving on a rough surface with a velocity of $16\,\mathrm{m/s}$. It covers a distance of $a$ of $20\,\mathrm{m}$ before coming to rest. Find the opposing force.

Solution:

$$m = 3\,\mathrm{kg} \text{ is mass of the object};$$ $$V_0 = 16\,\frac{\mathrm{m}}{\mathrm{s}} \text{ is initial speed of the object};$$ $$S = 20\,\mathrm{m} \text{ is covered distance};$$

Rate equation for the object:

$$0 = V_0 - a t$$ $$t = \frac{V_0}{a}$$

Equations of motion for the object:

$$S = V_0 t - \frac{a t^2}{2}$$

(1) in (2)

$$S = \frac{V_0^2}{a} - \frac{V_0^2}{2a} = \frac{V_0^2}{2a}$$ $$2aS = V_0^2$$ $$a = \frac{V_0^2}{2S}$$

Second Newton’s law along the X-axis for the object (F - opposing force):

$$F = m a$$

(3) in (4):

$$F = \frac{m V_0^2}{2S} = \frac{3\,\mathrm{kg} \cdot \left(16\,\frac{\mathrm{m}}{\mathrm{s}}\right)^2}{2 \cdot 20\,\mathrm{m}} = 58\,\mathrm{N}$$

Answer: opposing force is equal to $58\,\mathrm{N}$.