You may use g=10 m/s2 for gravity.
1. If a ball is thrown straight downward with an initial speed of
5 m/s, find its distance, velocity, and acceleration 3 seconds later. Neglect air friction, and assume that no forces other than gravity act on the ball.
2. The acceleration of a 2 kg mass in the x direction is given by
a = 12t2.
a. Find the expression for its velocity as a function of time and find
the velocity at 4 seconds.
b. Find the expression for its x position as a function of time
and its value at 4 seconds.
3. A force of 10 Newtons is exerted at an angle of 37° from the
x axis, and a 20 Newton force is exerted at 53°. These forces are exerted
on a 4 kg mass.
a. Find the magnitude and direction of the resultant force on the 4 kg mass.
b. Find the acceleration of the mass.
4. A ball is launched with an initial velocity of 100 m/s at an angle
of 37°. It is launched over level ground from zero height. What is
its height at time 2 seconds?
5. A 5 kg block is placed on an incline which makes an angle of 37° with the horizontal.
a. If the incline is frictionless, what is the acceleration of the mass
down the incline?
b. If the incline has a coefficient of friction m = 0.2, what would
be the frictional force which would resist the motion of the mass
down the incline?
6. Suppose you could swing a 5 kg mass around in a horizontal circle
on a frictionless surface with a rope. What tension in the rope would be
required to swing the mass in a 2 meter circle at 8 m/s constant speed?
7. You are holding a 4 kg mass, hanging on a rope. With what vertical
force must you pull on the rope to accelerate the mass upward at 4 m/s2?
8. A 20 kg mass sits on a surface with coefficient of friction 0.1.
A force of 35 N is exerted on the box at an angle of 37° upward above
the horizontal. What is the acceleration of the mass?
9. A 4 kg mass sits on a horizontal frictionless table and another 4
kg mass is tied to it by a string and suspended over a pulley. Find the
acceleration of the hanging mass.