Question

Find the mass and weight of a body if a resultant force of 850 N causes its speed to increase from 6 m/s to 15 m/s in a time of 5s.

Answer 1

Hi! Let's see.

TOPIC: Mass and Weight.

Step-by-step explanation:

Data:

• Force(F) = 850 N
• Initial Velocity(
  `\bold{V_(0)}`) = 6 m/s
• Final Velocity(
  `\bold{V_(f)}`) = 15 m/s
• Time(t) = 5 s
• Gravity(g) = 9.8 m/s²
• Mass(m) = ?
• Weight(w) = ?

==================================================================

In order to calculate the mass, we must first find the acceleration.

to find the acceleration, we apply the acceleration formula in UARM:

• 
  `\boxed{\boxed{\bold{a=(V_(f)-V_(0))/(t)}}}`

Replace per data:

• 
  `\boxed{a=(15(m)/(s)-6(m)/(s))/(5s)}}}`

We subtract in the numerator:

• 
  `\boxed{a=(9(m)/(s))/(5s)}}`

It divides:

• 
  `\boxed{\bold{a=1.8(m)/(s^(2))}}`

==================================================================

Mass

Knowing it's acceleration, we can proceed to calculate the mass, applying it's formula:

• 
  `\boxed{\boxed{\bold{m=(F)/(a)}}}`

Replace:

• 
  `\boxed{m=(850N)/(1.8(m)/(s^(2)))}}}`

Newton equivalents to kilograms:

• 
  `\boxed{m=(850kg*(m)/(s^(2)))/(1.8(m)/(s^(2)))}}}`

Simplify the m/s²:

• 
  `\boxed{m=(850kg)/(1.8)}}`

It divides:

• 
  `\boxed{\bold{m=472.22\ kg}}`

Answer: The mass of the body is 472.22 kilograms.

==================================================================

Weight

To calculate the weight, we use it's formula:

• 
  `\boxed{\boxed{\bold{W=m*g}}}}}`

Replace:

• 
  `\boxed{W=472.22*9.8(m)/(s^(2))}}}`

It multiplies:

• 
  `\boxed{\bold{W=4627.75\ N}}}}`

Answer: The weight of the body is 4627.75 Newtons.

Final Answer:

Mass = 472.22 kg

Weight = 4627.75 N.

Cordially Alejanndraax. Greetings!