Answer:
1. To find the force needed to accelerate a mass of 40 kg from one velocity to another in a given time, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) multiplied by the acceleration (a):
F = m * a
First, let's calculate the change in velocity (∆v) by subtracting the initial velocity (v1) from the final velocity (v2):
∆v = v2 - v1
= (8î + 3ĵ - 5k) m/s - (4î - 5ĵ + 3k) m/s
= (8î + 3ĵ - 5k) m/s - 4î + 5ĵ - 3k m/s
= 4î + 8ĵ - 8k m/s
Next, we divide the change in velocity (∆v) by the time (t) to calculate the acceleration (a):
a = ∆v / t
= (4î + 8ĵ - 8k) m/s / 10 s
= (0.4î + 0.8ĵ - 0.8k) m/s²
Finally, we calculate the force (F) by multiplying the mass (m) by the acceleration (a):
F = m * a
= 40 kg * (0.4î + 0.8ĵ - 0.8k) m/s²
= 16î + 32ĵ - 32k N
Therefore, the force needed to accelerate the 40 kg mass from the given velocities in 10 seconds is 16î + 32ĵ - 32k N.
2. The weight of an object is the force with which it is attracted towards the center of the planet or celestial body. On Earth, the weight of an object is given by the product of its mass (m) and the acceleration due to gravity (g):
Weight on Earth = m * g
Given that the man weighs 900 N on Earth, we can equate this weight to the product of his mass and the acceleration due to gravity on Earth (9.8 m/s²):
900 N = m * 9.8 m/s²
Solving for mass (m):
m = 900 N / 9.8 m/s²
≈ 91.84 kg
Now, to find the weight of the man on Jupiter, we need to know the acceleration due to gravity on Jupiter. Let's assume that the acceleration due to gravity on Jupiter is 24.8 m/s².
Weight on Jupiter = m * g (Jupiter)
= 91.84 kg * 24.8 m/s²
≈ 2276.35 N
Therefore, the weight of the man on Jupiter is approximately 2276.35 N.