Question

A 200g(m2) mass is pulling the cart (m1) across the table as shown below. If it covers 1.12m in 4.8 seconds starting from rest, what is the mass of the cart, assuming no friction?

Answer 1

Answer: 20.21 kg

Explanation:

The mass hanging from the pulley is pulling the cart. The force by which cart is being pulled is equal to weight of the hanging mass.

$F=m_2g$

⇒F=0.200 kg ×9.8 m/s²=1.96 N

Since there is no other force acting on the cart and there is no friction, so this force will pull the cart.

The Cart covers 1.12 m distance in 4.8 s.

From the equation of motion,

s = u t + 0.5 × a t²

We will find the acceleration of the cart,

Distance covered, s = 1.12 m

Initial velocity, u = 0 ( staring from rest)

Time taken, t = 4.8 s

⇒1.12 m = 0 + 0.5 × a × (4.8 s)²

⇒a = 0.097 m/s²

Now the force which causes this acceleration is:

F = ma

where m is the mass of the cart and a is the acceleration of the cart

⇒1.96 N = m×0.097 m/s²

⇒m = 20.21 kg

Hence, the mass of the cart is 20.21 kg.