A cyclist comes to a skidding stop in $10 \;m$. During this process, the force on the cycle due to the road is $200\; N$ and is directly opposed to the motion.
$(a)$ How much work does the road do on the cycle ?
$(b)$ How much work does the cycle do on the road ?
A cyclist comes to a skidding stop in $10 \;m$. During this process, the force on the cycle due to the road is $200\; N$ and is directly opposed to the motion.
$(a)$ How much work does the road do on the cycle ?
$(b)$ How much work does the cycle do on the road ?
Answer Work done on the cycle by the road is the work done by the stopping (frictional) force on the cycle due to the road.
$(a)$ The stopping force and the displacement make an angle of $180^{\circ} \quad(\pi \text { rad })$ with each other. Thus, work done by the road, $W_{r}=F d \cos \theta$
$=200 \times 10 \times \cos \pi$
$=-2000 J$
It is this negative work that brings the cycle to a halt in accordance with WE theorem.
$(b)$ From Newton's Third Law an equal and opposite force acts on the road due to the cycle. Its magnitude is $200 \,N$. However, the road undergoes no displacement. Thus, work done by cycle on the road is zero.
Similar Questions
A block of mass $m = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05.$ When hit by a bullet of mass $50\,g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac {v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,ms^{-2},$ the value of $H$ is close to ................. $\mathrm{km}$
A block of mass $m = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05.$ When hit by a bullet of mass $50\,g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac {v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,ms^{-2},$ the value of $H$ is close to ................. $\mathrm{km}$
- [JEE MAIN 2015]
Figure shows the variation of a force $F$ acting on a particle along $x$-axis. If the particle begins at rest at $x=0$, what is the particle's coordinate when it again has zero speed?
Figure shows the variation of a force $F$ acting on a particle along $x$-axis. If the particle begins at rest at $x=0$, what is the particle's coordinate when it again has zero speed?
Given that a force $\vec F$ acts on a body for time $t_1$ and displaces the body by $\vec d$ . In which of the following cases the velocity of the body must increase?
Given that a force $\vec F$ acts on a body for time $t_1$ and displaces the body by $\vec d$ . In which of the following cases the velocity of the body must increase?
On complete combustion a litre of petrol gives off heat equivalent to $3\times 10^7\,J$. In a test drive, a car weighing $1200\,kg$ including the mass of driver, runs $15\,km$ per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were $0.5$.
On complete combustion a litre of petrol gives off heat equivalent to $3\times 10^7\,J$. In a test drive, a car weighing $1200\,kg$ including the mass of driver, runs $15\,km$ per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were $0.5$.
A particle gets displaced by $\Delta \,\vec r = \,(2\hat i + 3\hat j + 4\hat k)$ $m$ under the action of a force $\vec F = \,(7\hat i + 4\hat j + 3\hat k)$ The change in its kinetic energy is ............... $\mathrm{J}$
A particle gets displaced by $\Delta \,\vec r = \,(2\hat i + 3\hat j + 4\hat k)$ $m$ under the action of a force $\vec F = \,(7\hat i + 4\hat j + 3\hat k)$ The change in its kinetic energy is ............... $\mathrm{J}$
- [AIEEE 2012]