Question

What is the mass of the cart with a constant net force of 200N is exerted to accelerate from rest to a velocity of 40m/s in 10s.

Answer 1

Answer:

$\bigstar{\bold{Mass\:of\:the\:cart=50\:kg}}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Force exerted (F) = 200 N
• Initial velocity (u) = 0 m/s
• Final velocity (v) = 40 m/s
• Time taken (t) = 10 s

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The mass of the cart (m)

$\Large{\underline{\underline{\it{Solution:}}}}$

$\dag$ First we have to find the acceleration of the cart

$\dag$ Acceleration is given by the formula,

 a = (v - u)/t

$\dag$ Substituting the data,

 a = (40 - 0)/10

 a = 40/10

 a = 4 m/s²

$\dag$ Hence acceleration of the cart is 4 m/s²

$\dag$ Now by Newton's second law of motion,

 F = m a

where

F = force acting on the object

m = mass of the cart

a = acceleration

$\dag$ Substituting the datas we get,

 200 = m × 4

 m = 200/4

 m = 50 kg

$\dag$ Hence mass of the cart is 50 kg

$\boxed{\bold{Mass\:of\:the\:cart=50\:kg}}$

$\Large{\underline{\underline{\it{Notes:}}}}$

$\dag$ Acceleration is the rate of change of velocity

 Acceration = ( Final velocity - Initial velocity)/Time taken

$\dag$ Newton's second law state that the rate of change of momentum is directly proportional to the force applied and the change takes place in the direction of the force.

 F = m a

Answer 2

Answer :-

★ The mass of the cart is = 50 Kg

★ Concept :

Here we can clearly see that we are given,the force applied on the body and change in velocity from rest to 40m/s in a certain time. So,we can firstly out the acceleration and thus apply the Newton's second Law of motion which is formulated as :-

F = m × a

• Force = mass × acceleration

★ Solution :

Given,

▶ Force applied on the body = F = 200 N

▶ Initial velocity of the body = u = 0 m/s

▶Final velocity of the body = v = 40 m/s

▶Time taken by the body to travel = t = 10 sec

✏ To find :-

• Primarily = Acceleration of the body

• Main answer = Mass of the body.

» Let the acceleration of the cart be 'a'.

» Also let the mass of the cart be 'm'.

Now, let's find out the acceleration.

Using Newton's First Equation of Motion,

• v - u = at

By applying, values, we get,

✒ (40) - (0) = a × 10

✒ a × 10 = 40

▶ $a \: \: = \: \: (\dfrac{40}{10})$

✒ a = 4 m/s²

By rechecking the units, we get,

• Acceleration of the cart = a = 4 m/s²

Now, let us find the mass of the cart.

Using the Newton's Second Law of Motion,

• Force = Mass × Acceleration

• F = m × a

By applying, values in the formula we get,

✒ 200 N = m × 4 m/s²

✒ m × 4 = 200

▶ $m \: \: = \: \: \dfrac{200}{4}$

✒ m = 50 Kg

▶ On rechecking the units of equation, we get, our answer as :-

Mass of the cart = 50 Kg

So, our required answer = 50 Kg.

★ More to know :-

• Newton's second Law of Motion - It states that the rate of change of momentum of a body is directly proportional to rhe external force applied of the body and the change takes place in the direction of motion.

• The larger the force acting on the body, greater is the change in momentum.

• Note* here the mass of the body will be in Kg. Since, the acceleration is in m/s² , but the force is given in N. So, if the mass of the cart be in g, then the force should have been in Dyne (CGS unit). So our answer is correct.