(Q1)How much work is done when a bucket of mass 1.5kg with 10g of water in it is pulled up from the bottom of a well 8m deep? Take g=9.8m/s2 (a)100.3j(b)2000.5j(c)901.6j(d)453.7j (Q2) A 65kg sprinter completes a 100m race in 9.83s. Calculate the average kinetic energy of the spinter. (a)3.36kj(b)2.11kj(c)34.15kj(d)65.42kj
Q1
1kg = 1000 g
It does not make sense to use a bucket of 1.5kg to pull up 10 g of water. You must mean 10 kg of water.
1.5kg+10kg=11.5 kg
Work done = mgh (in consistent units)
=11.5*9.8*8 j
Q2
The word "average" has been used very vaguely. If it means to calculate the kinetic energy of the sprinter using the average speed, then it would be:
average speed=100m / 9.83 s. =10.1729 m/s
kinetic energy
=mv²/2
=65*10.1729²/2 (approx.) joules
14 Given that the mass and radius of Jupiter are respectively 1 90 1027kg and 7 15 104km, calculate the escape velocity from the surface of the planet
100.3j
To answer these questions, we need to use the relevant formulas and known values. Let's go through them one by one:
Q1) To calculate the work done, we can use the formula:
Work = Force * Distance * cos(theta),
where Force is the weight of the bucket, Distance is the vertical distance traveled, and theta is the angle between the force vector and the displacement vector.
First, let's calculate the weight of the bucket which is given by:
Weight = mass * gravity,
where mass is the mass of the bucket and water.
Given that the mass of the bucket is 1.5kg and the mass of water is 10g (which is 0.01kg), the total mass is 1.5kg + 0.01kg = 1.51kg.
Plugging in the values, we get:
Weight = 1.51kg * 9.8m/s^2 = 14.798N.
Now, let's calculate the work done:
Work = 14.798N * 8m * cos(0°) [since the force and displacement are in the same direction],
Work = 14.798N * 8m * 1,
Work = 118.384J.
Therefore, the work done when the bucket is pulled up from the well is 118.384J, which is not one of the given options. It might be worth double-checking the options or the calculations.
Q2) To calculate the average kinetic energy, we can use the formula:
Average Kinetic Energy = (1/2) * mass * velocity^2.
Given that the mass of the sprinter is 65kg and the time taken for the race is 9.83s, we need to calculate the velocity using the formula:
velocity = distance / time,
velocity = 100m / 9.83s,
velocity ≈ 10.17m/s.
Now, let's calculate the average kinetic energy:
Average Kinetic Energy = (1/2) * 65kg * (10.17m/s)^2,
Average Kinetic Energy ≈ 3.36kJ.
Therefore, the average kinetic energy of the sprinter is approximately 3.36kJ, which corresponds to option (a) in the given choices.
Note: Make sure to double-check the options and your calculations for the first question, as the provided options do not match the calculated value.