Question

A large block is held at rest on a frictionless surface and attached by a string to a small block that
hangs in the air, as shown in the picture. The large block is released and slides on the surface a
distance of 2.24 meters in 1.74 seconds. The mass of the small block is 50.0 grams. Find the mass
of the large block.

Answer 1

Newton's third law of motion states that the action of a force is equal and opposite to the reaction to the force

• The mass of the large block is approximately 281.48 kg

Reason:

The given parameters are;

The distance the to which the large block slides, s = 2.24 meters

Time in which the block slides, t = 1.74 seconds

Mass of the small block, m = 50.0 grams

Mass of the large block, M = Required

Solution:

The distance covered, s in time, t, is given by the relation;

$s = u\cdot t + \dfrac{1}{2} \cdot a \cdot t^2$

Where;

u = The initial velocity = 0

a = The acceleration

Which gives;

• $a = \dfrac{2 \cdot s}{t^2}$

Therefore;

$a = \dfrac{2 \times 2.24}{1.74^2}\approx 1.48$

• The acceleration of the two masses, a ≈ 1.48 m/s²

The applied force = The weight of the small mass = m·g

The masses moved at the acceleration, a =1.48 m/s², are M + m

Where;

M = The mass of the large block

∴ m·g = a·(M + m)

• $M = \dfrac{m \cdot g}{a} - m$

Which gives;

$M = \dfrac{50 \times 9.81}{1.48} - 50 \approx 281.48$

• The mass of the large block, M ≈ 281.48 kg

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