91Ó°ÊÓ

When we think about work done in physics, it usually involves a force causing an object to move. In the case of the snowball falling from the cliff, gravity is responsible for this force. Work done by gravity is defined as the force of gravity acting on an object as it travels across a certain distance. In our example, gravity does work on the snowball by pulling it downwards from the height of the cliff to the ground. This can be quantified using the equation:\[ W = mgh \]where:

• \( W \) is the work done by gravity
• \( m \) is the mass of the snowball (1.50 kg)
• \( g \) is the acceleration due to gravity (approximately 9.8 m/s²)
• \( h \) is the height of the cliff (12.5 m)

Plug in the values and calculate: \( W = 1.50 \times 9.8 \times 12.5 = 183.75 \) Joules. The positive sign indicates that gravity is doing positive work in the direction of the motion.

Gravitational potential energy is the energy stored by an object due to its position relative to the ground. This energy is released when the object moves and can be computed using the formula: \[ U = mgh \]This represents the potential energy at a height above a reference point. For the snowball launched from the cliff, the potential energy at the top is non-zero since it is elevated.When the snowball falls to the ground, the gravitational potential energy is converted into kinetic energy. The change in gravitational potential energy corresponds to the work done by gravity. Therefore, \[ \Delta U = -mgh \]This indicates that 183.75 Joules of potential energy are lost when the snowball descends to ground level, and a negative sign simply shows this decrease.

Projectile motion describes the movement of an object thrown into space under the influence of gravity. It's a combination of two motions:

• Horizontal motion at a constant speed
• Vertical motion under constant acceleration due to gravity

In our exercise, the snowball is fired with an initial velocity at an angle of 41° above the horizontal. This initial velocity can be broken into horizontal and vertical components using trigonometry:- Horizontal component: \( v_{x} = v\cos(\theta) \)- Vertical component: \( v_{y} = v\sin(\theta) \)where \( v \) is the initial speed (14.0 m/s) and \( \theta \) is the angle of projection (41°). Calculating these components allows us to analyze how the snowball travels through the air.As it moves, the snowball is accelerated vertically by gravity, affecting the trajectory until it reaches the flat ground. Understanding these principles helps in comprehending the motion and behavior of projectiles.