A particle of mass 100g is thrown vertically upwards with a speed of 5m/s, the work done by the force of gravity during the time the particle goes up

The work done by a force is given by the formula:

W = F * d * cos(θ)

where:

• W is the work done,
• F is the force,
• d is the distance (or displacement),
• θ is the angle between the force and the displacement.

In this case, the force is the force of gravity, which is equal to the mass of the object times the acceleration due to gravity (F = m * g). The mass m is 100g = 0.1kg, and the acceleration due to gravity g is approximately 9.8m/s². So, the force of gravity is F = 0.1kg * 9.8m/s² = 0.98N.

The displacement d is the distance the particle travels upwards. This can be found using the equations of motion. The initial velocity u is 5m/s, the final velocity v is 0m/s (because the particle stops moving upwards at the highest point), and the acceleration a is -g (because it's acting downwards). Using the equation v² = u² + 2ad, we can solve for d:

0 = (5m/s)² + 2*(-9.8m/s²)d d = (5m/s)² / (29.8m/s²) = 1.28m

The angle θ between the force of gravity and the displacement is 180°, because the force of gravity acts downwards while the displacement is upwards. The cosine of 180° is -1.

So, the work done by the force of gravity is:

W = F * d * cos(θ) = 0.98N * 1.28m * -1 = -1.25J

The work done is negative because the force of gravity is doing work against the motion of the particle.