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.

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) = ?

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

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

• $\boxed{\boxed{\bold{a=\frac{V_{f}-V_{0}}{t}}}}$

Replace per data:

• $\boxed{a=\frac{15\frac{m}{s}-6\frac{m}{s}}{5s}}}}$

We subtract in the numerator:

• $\boxed{a=\frac{9\frac{m}{s}}{5s}}}$

It divides:

• $\boxed{\bold{a=1.8\frac{m}{s^{2}}}}$

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Mass

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

• $\boxed{\boxed{\bold{m=\frac{F}{a}}}}$

Replace:

• $\boxed{m=\frac{850N}{1.8\frac{m}{s^{2}}}}}}$

Newton equivalents to kilograms:

• $\boxed{m=\frac{850kg*\frac{m}{s^{2}}}{1.8\frac{m}{s^{2}}}}}}$

Simplify the m/s²:

• $\boxed{m=\frac{850kg}{1.8}}}$

It divides:

• $\boxed{\bold{m=472.22\ kg}}$

Answer: The mass of the body is 472.22 kilograms.

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Weight

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

• $\boxed{\boxed{\bold{W=m*g}}}}}$

Replace:

• $\boxed{W=472.22*9.8\frac{m}{s^{2}}}}}$

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!