Question

1. A person standing on the surface of the earth has a weight of 650 N.
a) What is its weight at a distance of two earth radii from the surface? b) Assume the same person is standing on a planet that has twice the mass, but half the radius of Earth. What would be her/his weight?
2. A force F = 500N is applied on a mass m and leads to an acceleration of a = 5m/s2. a) What is the value for the mass m? b) How much force must be applied to a mass of 5m to obtain twice the acceleration (a = 10m/s2)?
3. A pillow of mass m = 1.5kg travels with a speed v = 5m/s before it hits at PHYS1010 student. The pillow comes to rest (stops) within a time interval of ∆t = 0.2s a) How big is the force that our student feels? b) we redo the fight with a stainless steel pillow of the same mass. This time the pillow comes to rest in 0.02 s. How big is the force this time?

Answer 1

1) given that

weight on earth surface We = 650 N

We = mg

here g = GM/r^2

a) when the radius is twice g becomes 1/4 times that of on earth value

so weight = 650/4 = 162.5 N

b) if mass becomes twice and radius becomes half

weight = 2*m*GM/(r/2)^2 = 8mg = 8*650 = 5200 N

2) a) mass m = f/a = 500/5 = 100 kg

b) force f' = 5*100*2*10 = 10000 N

3) a) force f = mv/∆t

f = 1.5*5/0.2 = 37.5 N

b) f = 1.5*5/0.02 = 375 N