Kinetics and dynamics questions?

Question

1) A 900kg car traveling at 105 km/h runs into a tree and comes to a stop in 700ms. what is the average force exerted on the tree?

2) A rocket mass 500kg is propelled vertically upwards by a motor producing a force of 7kN. What is its acceleration?

3) An artificial satellite is placed in a circular orbit with a peroid of 16.0 days around Larissa, a moon of neptune. An on-board altimeter measures the distance to the surface of Larissa to be 2500km, which is much greater than the radius of the moon. Estimate Larissa's mass.

Please show workings and the general equations used to work them out. Many thanks in advance

Answer 1

1) First calculate the deceleration.
v=u+at
v =0
u=10km/h = 25/9 m/s

0=25/9 + a(700x10^-3)
a=- 3.968253968 m/s²

F=ma
Force = 900 x ( 3.968253968)
Force = - 3571.428571 N
Force is opposing motion that why its negative .

2) F=ma
Driving force - Weight = mass x acceleration
7000 - (500x9.8) = 500a
2100=500a
acceleration = 4.2m/s²

3)
F=Gm1m2/R²
F=m(w)²R
m2(w)²R=Gm1m2/R²
(2π/T)²R=Gm1/R²
(2π/T)²R³=Gm1
(2π/16x24x60x60)²(2500x10³)³=(6.67x10^-11)m1
mass = 4.839343821x10^18 Kg

Answer 2

1) A 900kg car traveling at 105 km/h runs into a tree and comes to a stop in 700ms. what is the average force exerted on the tree?

dp = F t; where dp = m dv the change in momentum upon crashing, t = .7 sec the time over which the momentum changed, and F is the force you are looking for. Thus, F = dp/t and the change in momentum dp = 900*105 kg-km/hr change all this into kg-m/sec and solve for F in Newtons.

2) A rocket mass 500kg is propelled vertically upwards by a motor producing a force of 7kN. What is its acceleration?

Net force acting on the rocket f = Ma = F - W = F - Mg; where W = Mg the weight of the rocket. Then a = F/M - g. Note a <> constant during the ascent because the rocket fuel mass (m) will burn off making the total mass M = m + n get smaller during the ascent; where m is fuel mass and n is frame mass. Thus acceleration (a) found for F = 7,000 N and M = 500 kg is only for that level of total mass.

3) An artificial satellite is placed in a circular orbit with a peroid of 16.0 days around Larissa, a moon of neptune. An on-board altimeter measures the distance to the surface of Larissa to be 2500km, which is much greater than the radius of the moon. Estimate Larissa's mass.

Centrifugal force m w^2 R = GmM/R^2 the force of gravity on the satellite of mass m from the moon of mass M, which is what you are looking for; so that (1/T)^2 R^3 = GM; where R = r + h and r is the moon's radius and h = 2500 km. If h >>> r then we can approximate R = h. Then M = (1/T)^2 h^3/G where G is the gravity constant you can look up. 1/w = T = 16 days the period where w is the angular velocity of the satellite. You can do the math...make sure your units are kg-m-sec units when you do the arithmetic.