A toy gun fires a plastic pellet with a mass | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: Mass $m = 0.5\ g = 0.5 	imes 10^{-3}\ kg$, Spring constant $k = 1.25\ N/cm = 125\ N/m$, Compression $x = 2.0\ cm = 0.02\ m$, Distance $d =

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) Given: Mass $m = 0.5\ g = 0.5 	imes 10^{-3}\ kg$, Spring constant $k = 1.25\ N/cm = 125\ N/m$, Compression $x = 2.0\ cm = 0.02\ m$, Distance $d = 10\ cm = 0.1\ m$, Friction force $f = 0.0475\ N$.According to the Work-Energy Theorem, the work done by the spring minus the work done against friction equals the change in kinetic energy:$W_{spring} - W_{friction} = \Delta K$$\frac{1}{2} k x^2 - f d = \frac{1}{2} m v^2$Substituting the values:$\frac{1}{2} 	imes 125 	imes (0.02)^2 - 0.0475 	imes 0.1 = \frac{1}{2} 	imes 0.5 	imes 10^{-3} 	imes v^2$$0.5 	imes 125 	imes 4 	imes 10^{-4} - 0.00475 = 0.25 	imes 10^{-3} 	imes v^2$$0.025 - 0.00475 = 0.25 	imes 10^{-3} 	imes v^2$$0.02025 = 0.25 	imes 10^{-3} 	imes v^2$$v^2 = \frac{0.02025}{0.25 	imes 10^{-3}} = \frac{20.25}{0.25} = 81$$v = 9\ m/s$.

Similar Questions

$A$ car and a truck are moving with the same kinetic energy. If the same retarding force is applied to both by using brakes,what will be the distance traveled by both vehicles before coming to rest?

$A$ car driver is trying to jump across a path as shown in the figure by driving horizontally off a cliff '$X$' at a speed of $10 \ m \ s^{-1}$. When he touches peak '$Z$' (ignore air resistance), what would be his speed (in $m \ s^{-1}$)? (use $g = 10 \ m \ s^{-2}$)

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$, where $x$ is in meters and $t$ is in seconds. Find the work done in the first $6$ seconds. (in $\text{ J}$)

$A$ ball of mass $300 g$ is dropped from a height $10 m$ above a sandy ground. On reaching the ground,it penetrates through a distance $1.5 m$ in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $= 10 m s^{-2}$) (in $N$)

$A$ simple pendulum is released from $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module