Question

6. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its

potential energy? If the object is allowed to fall, find its kinetic energy when it is half

way down (g = 10 m/s26. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its

potential energy? If the object is allowed to fall, find its kinetic energy when it is half

way down (g = 10 m/s​

Answer 1

Explanation:

Given:

• Mass of an object (m) = 40 kg
• Height (h) = 5 m

To find:

• Potential energy (P.E) = ?
• Kinetic enery (K.E) when it is half way down = ?

Solution:

▪︎We remember that, $\blue{\sf{potential\:energy (P.E) = mgh}}$

$\implies$ P.E = 40 × 10 × 5

$\implies$ P.E = 400 × 5

$\implies\:\sf{\underline{\underline{\therefore\:Potential\:energy\:is\:2,000\:J\:or\:2\:kJ}}}$

▪︎We also know that, $\green{\sf{kinetic\:energy\:(K.E)\:=\:\dfrac{1}{2}mv^2}}$

We are not given with the velocity (v) but we know that if anything is thrown vertically upwards the final velocity will be 0 m/s,we need to find initial velocity (u). In this case, we have to find K.E half way down, means height = h/2.

h/2 = 5/2 = 2.5 meters.

We know, Newton's third equation of motion i.e, v² = u² + 2gh

$\longrightarrow$ 0² = u² + 2 × 10 × 2.5

$\longrightarrow$ 0² = u² + 2 × 25

$\longrightarrow$ -50 = u²

$\longrightarrow\:\sf{\sqrt{50}\:=\:u}$

$\longrightarrow$ 7.07 m/s = u

Now, we know the velocity with which it was thrown find the kinetic energy.

$\implies\:\sf{K.E\:=\:\dfrac{1}{2}\:×\:40\:×\:(7.07)^2}$

$\implies$ K.E = 20 × 49.9849

$\implies\:\sf{\underline{\underline{\therefore\:K.E\:is\:989.698\:Joules}}}$

Answer 2

$\green{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

Potential energy of an object is the energy in it due to it's position. It is defined as the product of mass, acceleration and the height from ground or something. It is defined by the expression :

$\bigstar \: \orange{\mid{\underline{\overline{\textbf{p = mah}}}\mid}}$

Kinetic energy is the energy of an object due to it's motion. It is defined as half of product of mass and square of velocity of a body. It is defined by the expression ;

$\bigstar \: ke = \frac{1}{2} \times m {v}^{2}$

$\blue{\mid{\underline{\overline{\textbf{Coming to question :-}}}\mid}}$

In this question we have been given an object of particular mass which is raised to a particular height, the potential energy of object at that point is not known and the kinetic energy in half of its way when it falls. We have to calculate both.

Important keywords :

• Mass of object = 40kg
• Height till raised = 5m
• Acceleration due to gravity = 10m/s^2

Now, the potential energy of object will be :

$\bigstar \: pe = mah$

After inputting the known values in this expression we get:

$\mapsto \: pe = 40 \times 10 \times 5$

$\mapsto \: pe = 2000joule$

Since 1KJ = 1000J, Thus

$\mapsto \: pe = 2kj$

Therefore we got potential energy of object to be 2Kj (Kilojoule).

Now, at maximum height of any vertically thrown object its final velocity becomes Zero and when it falls down its final velocity becomes is initial velocity that is Zero.

In this case object reached 5m and started to fall down, Now at 5m its velocity would be = 0 , and when its falling this is equal to it's initial velocity.

Now, we have for the object :

• Initial velocity = 0
• Final velocity = v = ?
• Mass = 40kg
• Acceleration = 10
• Given distance to calculate Kinetic energy = 5m /2 = 2.5m

Now according to third equation of motion :

$\bigstar \: {v}^{2} = {u}^{2} + 2as$

In this equation :

• v = Final velocity
• u = Initial velocity
• A = Acceleration
• s = distance or displacement

Now after inputting the known values in this equation we get :

$\mapsto \: {v}^{2} = 0 + 2 \times 10 \times2.5$

$\mapsto \: {v}^{2} = 50$

$\mapsto \: v = \: \sqrt{50} = 7.07$

Therefore we calculated the final velocity of object is 7.07m/s.

Now after inputting the values in kinetic energy formula we get, its kinetic energy to be :

$\mapsto \: \frac{1}{2} \times m {v}^{2}$

$\mapsto \: \frac{1}{2} \times 40 \times {7.07}^{2}$

$\mapsto \: 20 \times 49.9$

$= 999.69j$

Therefore we got kinetic energy of object to be 999.69Joules.

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