Question

1. While enter a highway, a car accelrates from 15.m/s to 32.0m/s at a rate of 2.90m/s^2. a. how far did the car travel while accelerating? b. how long did it take the car to accelerate from 15.0m/s to 32.0m/s^2

2.Using Newton's law of gravity, calculate the weight of a 90.0kg astronaut standing on the surface of a planet that has the same mass as the earth, but only half the radius of the Earth.

3. a 3,00kg pickup truck is moving at a sped of 12.0m/s when it collides intop the back of a 2,200kg car which was moving in the same direction as the truck with a velocity of 2.00m/s. After the collision, the truck continues forward but is slowed down to a velocity of 5.00m/s. What is the velocity of the car immediately after the collision?

4.A certain machine part rotates at a rate of 2,000rev/min when operating at full speed. When the machine is shut off the part takes 25 seconds to come to a complete stop. A. What is the angular acceration of the machine part? B. Through what angle (in radians) will it turn while it slows down to a stop?

Answer 1

1) v^2 - u^2 =2aS

32^2 - 15^2 = 2*2.9*S

S = 137.75 m

b) v = u + at

32 = 15 + 2.9*t

t = 5.86 s

2) g = 9.8 m/s2 on earth's surface

g = GM/r^2

g = GM/(r/2)^2 = 4GM/r^2

g = 4*9.8 = 39.2 m/s23

Weight = mg = 90*39.2 = 3528 N

3) By the conservation of momentum we have

m1u1 + m2u2 = m1v1 + m2v2

300*12 +2200*2 = 300*5 + 2200v2

v2 = 2.95 m/s

velocity of car after the collision = 2.95 m/s

4) a)w = 2piN/60 = 2pi*2000/60 = 209.44 rad/s

angular acceleration = w/t = 209.44 / 25 = -8.37 rad/s2

angle turned = (w^2 - wo^2)/2

= (0 - 209.44^2) / 2*-8.37

= 2618 rad