Question

Which would require a greater force - accelerating a 2 kg mass at
$5ms ^{ - 2} or \: a \: 4kg \: mass \: at \: {2ms}^{ - 2}$
​

Answer 1

Answer:

Object 1 [The object which has mass 2 kg which is accelerating at 5 m/s².]

Explanation:

As per the provided information in the given question, we have :

• An object of mass 2 kg is accelerating at 5 m/s².
• An object of mass 4 kg is accelerating at 2 m/s².

We've been asked to calculate which would require a greater force.

In order to calculate which would require a greater force, we need to calculate the force required by both objects. After that, by comparing we'll find which would require a greater force.

Here,

• m₁ = 2 kg
• m₂ = 4 kg
• a₁ = 5 m/s²
• a₂ = 2 m/s²

$\large {\underline { \sf {Force \; required_{(By \; Object \; 1)} :}}}$

$\bigstar \quad \underline{\boxed{ \bf {F_1 = m_1 \times a_1}} }$

• F₁ denotes force required by 1st object
• m₁ denotes mass of the first object
• a₁ denotes acceleration of the first object

$\dashrightarrow \quad \rm { F_1 = (2 \times 5) \; N}$

$\dashrightarrow \quad \boxed{ \rm { F_1 =10 \; N\dots \; (1) } }$

$\large {\underline { \sf {Force \; required_{(By \; Object \; 2)} :}}}$

$\bigstar \quad \underline{\boxed{ \bf {F_2 = m_2 \times a_2}} }$

• F₂ denotes force required by second object
• m₂ denotes mass of the second object
• a₂ denotes acceleration of the second object

$\dashrightarrow \quad \rm { F_2 = (4 \times 2) \; N}$

$\dashrightarrow \quad \boxed{ \rm { F_2 =8 \; N\dots \; (2) } }$

Now, by comparing force required by both objects. We get,

• F₁ > F₂

∴ The first object will require greater force.

$\rule{200}2$

Answer 2

Answer:

We have F = ma.

Here we have,

$m_{1} = 2kg; a_{1} = 5m {s}^{ - 2}$

$and \: m_{2} = 4kg ; a_{2} = 2m {s}^{ - 2}$

Thus,

$f_{1} = m_{1} a_{1} = 2kg \times 5m {s}^{ - 2} = 10N;$

$and \: f_{2} = m_{2} a_{2} = 4kg \times 2m {s}^{ - 2} = 8N.$

$= > F_{1} > F_{2}$

Thus,

$accelerating \: a \: 2 \: kg \: mass \: at \:$

$5m {s}^{ - 2} \: would \: require \: a \: greater \: force.$