[3 Mark Question Answer]

Question 13 Marks

What is meant by mechanical energy ? Explain in detail.

Answer

The energy possessed by a body due to the work done on it is known as mechanical energy. When work is done on a body, another body supplies the force to do the work. For example, when you lift a stone from the ground, your body supplies the force which raises the height of the stone from the ground $($work done$)$. In doing the work, your body spends some energy. As energy is neither created nor destroyed, some of the energy spent by your body is gained by the stone. This energy is the mechanical energy.

Work is done on a body when the body is displaced. So, the energy gained by a body due to its state of motion or due to its position is known as mechanical energy. Mechanical energy is of two types $—$ kinetic energy or energy in action and potential energy or stored energy. These two forms of energy are readily changeable from one form to the other.

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Question 23 Marks

A person does $5000\ J$ of work in climbing a tree of height $5\ m$. Calculate the mass of the person.

Answer

Mass of the person$, m = ?$
Height of the tree$, h = 5\ m$
Work done by the person$, W = 5000\ J$
From work$-$energy relationship, we can say that the work done by the person in climbing the tree against gravity gets stored in him as gravitational potential energy.
Potential energy of the person$, P.E. = W = 5000\ J$
From the formula$, P.E. = mgh$
we get$, 5000\ J = m \times (10\ m/s^2) \times (5\ m)$
or $m = 100 \ kg$

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Question 33 Marks

What is the speed of a runner of mass $50 \ kg$ whose kinetic energy while running is $2500 \ J$?

Answer

Mass of a runner$, m = 50 \ kg$
Speed of the runner$, v = ?$
Kinetic energy of the runner$, K.E. = 2500 \ J$
From the formula,
$K.E. = 12\ mv^2$
We get,
$2500 \ J = 12 \times (50 \ kg) \times v^2$
$2500 \ J = 25 \ kg \times v^2$
or $v^2 = 100\ m^2/s^2$
or $v^2 = 100\ m/s$

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Question 43 Marks

Which factor will have a greater effect on the kinetic energy of an object, doubling its mass or doubling its velocity?

Answer

Let mass of an object be m and its velocity be $v$.
Kinetic energy of the object, $ K.E. =\frac{1}{2} mv ^2$
When the mass is doubled, kinetic energy $=\frac{1}{2}(2 m) v^2=m v^2$
When the velocity is doubled, kinetic energy $=\frac{1}{2} m (2 v )^2=2 mv ^2$
Doubling the velocity of an object will have greater effect on its kinetic energy than doubling its mass.

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Question 53 Marks

A man is walking with a suitcase held in his hand.
$a.$ Why is no work done on the suitcase if the man is walking on a horizontal platform?
$b.$ Why is work said to be done if the man is climbing a staircase?

Answer

a:If a man carrying a suitcase is walking on a horizontal platform, the suitcase moves. But the force applied $($force of gravity$)$ on the suitcase is in the vertically downwards direction, whereas, its displacement is in the horizontal direction. A vertical force can never cause a horizontal displacement. So the displacement of the suitcase is not due to the force of gravity acting on it. Therefore, no work is done by the force of gravity in this case.
b:if a man carrying a suitcase climbs up a staircase, then work is done to carry the suitcase against the force of gravity.

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