Question

A trolley of mass 1000 kg is moving with a speed of 5 m/s. Sand is dropped onto it at the rate of 30 kg/minute. What is the Force required to keep the trolley moving with a uniform speed.

(grade 11, Phy , ch:LAWS OF MOTION)

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Answer 1

Solution :-

As per the given data ,

• mass of the trolley = 1000 kg
• speed of the trolley = 5 m/s
• sand dropped at a rate of = 30 kg / min

We need to find the force required to keep the trolley moving with uniform speed

Force is the rate of change of momentum,

$\bigstar\boxed{\mathtt{\pink{F = \dfrac{dP}{dt}}}}....(1)$

here ,

• F = force
• P = momentum
• t = time

Momentum is given by the formula ,

$\bigstar\boxed{\mathtt{\pink{P= mv}}}...(2)$

here ,

• m = mass
• v = velocity

Now let's substituting (2) in (1) ,

$\implies\mathtt{F = \dfrac{d(mv)}{dt}}$

we know that ,

$\bigstar\boxed{\mathtt{\pink{\dfrac{d(vu)}{dt}= v\dfrac{du}{dt}+u\dfrac{dv}{dt}}}}$

From the above equation we can conclude that ,

$\implies\mathtt{F = m\dfrac{dv}{dt}+v\dfrac{dm}{dt}}$

As  the trolley is moving with uniform speed ,

$\implies\mathtt{\dfrac{dv}{dt}= 0 }$

Hence ,

$\implies\mathtt{F = m\times 0 +v\dfrac{dm}{dt}}$

$\implies\mathtt{F = v\dfrac{dm}{dt}}$

As per the given data ,

$\implies\mathtt{\dfrac{dm}{dt}= 30\dfrac{kg}{min} }$

We first need to convert it into kg / sec in order to do that simply divide by 60

$\implies\mathtt{\dfrac{dm}{dt}= \dfrac{30}{60} = \dfrac{1}{2}\dfrac{kg}{sec} }$

$\implies\mathtt{F = 5 \times \dfrac{1}{2} }$

$\implies\mathtt{\red{F =2.5 \:N }}$

The force required to keep the trolley moving with uniform speed is 2.5 N

Answer 2

Answer:

(2) Mass of electron = 9.1 × 10–31 kg 10–30 kg (as 9.1 > 5). ... Magnitude of force experienced by an object moving with speed v is given ... direction of acceleration remain constant.