Calculate the force needed to accelerate a 1 kg ball by 3 m/s:
a. in space along way from the earth.
b. on the ground in a direction horizontal to the ground.
c. on the earth vertically upward.
To calculate the force needed to accelerate an object, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).
In this case, we'll use the equation F = m x a, where:
- F is the force in Newtons (N)
- m is the mass of the ball in kilograms (kg)
- a is the acceleration in meters per second squared (m/s²)
Let's calculate the force needed for each scenario:
a. In space, far from the Earth:
Since there is no gravity or significant external forces acting on the ball in space, the force required to accelerate it is simply given by the equation F = m x a. Therefore, the force needed to accelerate a 1 kg ball by 3 m/s in space is:
F = 1 kg × 3 m/s² = 3 N
b. On the ground, in a horizontal direction:
When the ball is on the ground and we want to accelerate it horizontally, we need to take into account the force of friction. Assuming there is no air resistance, the force of friction is approximately negligible. Therefore, the force required to accelerate the ball horizontally is still given by F = m x a. Thus, the force needed to accelerate a 1 kg ball by 3 m/s horizontally on the ground is:
F = 1 kg × 3 m/s² = 3 N
c. On the Earth, vertically upward:
When accelerating an object vertically on Earth, we need to consider the force of gravity acting in the opposite direction. The force of gravity on a 1 kg object is approximately 9.8 N (rounded to one decimal place). To accelerate the ball upward against gravity, we need to overcome this force. Therefore, the force needed to accelerate a 1 kg ball by 3 m/s vertically upward on Earth is:
F = m x (a + g) = 1 kg × (3 m/s² + 9.8 m/s²) ≈ 12.8 N
So, to summarize:
a. In space: 3 N
b. On the ground horizontally: 3 N
c. On Earth vertically upward: approximately 12.8 N