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In this lesson, we will learn how to calculate the weight of an object given its mass and its distance from an astronomical body.

Q1:

A body of mass 1 . 0 0 × 1 0 2 kg was weighed, using a spring scale, at the north pole and at the equator. Assuming 𝑔 = 9 . 8 3 m/s^{2} at the north pole and 𝑔 = 9 . 7 8 m/s^{2} at the equator, what was the difference in the two readings?

Q2:

The force exerted by the Moon’s gravity at its surface is six times smaller than the force exerted by the Earth’s gravity at its surface. The weight of an astronaut plus his space suit on the Moon is 250 N.

How much does the suited astronaut weigh on Earth?

What is the mass of the suited astronaut on the Moon?

What is the mass of the suited astronaut on Earth?

Q3:

Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted, and an astronaut’s acceleration is measured to be 0.893 m/s^{2}. Calculate her mass.

Q4:

The mass of a particle is 15.0 kg.

What is its weight on Earth?

On the Moon, the acceleration produced by gravity is 1.63 m/s^{2}. What is its weight of the particle on the Moon?

What is its mass on the Moon?

What is its weight in outer space far from any celestial body?

What is its mass at this point?

Q5:

A service elevator carries a load of garbage with a mass of 24.4 kg. the elevator accelerates vertically downward at 1.8 m/s^{2}. What is the magnitude of the force the garbage exerts on the floor of the elevator?

Q6:

A ball with a mass of 0.25 kg is thrown vertically upward toward a gym ceiling. As it comes into contact with the ceiling, a force of 78.0 N is applied to it for 0.02 s, causing it to rebound downward. Which of the following is true as the ball is falling to the floor again?

Q7:

When landing after a spectacular somersault, a 45.0 kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 6.00 times the acceleration due to gravity.

Q8:

Calculate the force a 70.0 kg high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity.

Q9:

A uniformly cylindrical tube that is open at both ends has a diameter of 16 cm. Two spheres are at rest inside the tube, as shown in the accompanying diagram. The diameters of the spheres are 8 cm and 12 cm respectively and the spheres weigh 10 N and 30 N respectively. Calculate the minimum weight of the tube for the system of the tube and spheres to be in equilibrium.