Dynamics
What does Sigma F equal?
mass*acceleration
What does the centripetal force equal?
(mass*velocity^2)/radius
What are the formulas for:
GPE
KE
EPE
GPE: mgh
KE: 1/2mv2
EPE: 1/2kx2
What does Sigma Torque equal?
Moment of Inertia x angular accceleration
OR
Force x Radius
What is the equation for Gravitational Force?
F=GMm/r^2
A box of mass m is sliding down an incline where the coefficient of kinetic friction between the box and the incline uk. Draw a free body diagram with all forces acting on the box.
(Draw as needed)
A ball of mass M attached to a string of length L moves in a circle in a vertical plane. At the top of the circular path, the tension in the string is twice the weight of the ball. At the bottom, the ball just clears the ground. Air resistance is negligible. Express all answers in terms of M, L, and g.
Determine the magnitude and direction of the net force on the ball when it is at the top.
3Mg, directed down
A calculator of mass 0.11 kg is lowered from a bookshelf that is 1.6 m above the floor to a desk that is 0.85 m above the floor. What is its change in GPE?
-0.81 Joules
A boy pulls a wagon in a circle. The wagon starts from rest and accelerates to an angular velocity of 0.25 rad/s in 1.2 s. What is the wagon’s angular acceleration?
0.21 rad/s^2'
The Sojourner rover vehicle was used to explore the surface of Mars as part of the Pathfinder mission in 1997. Mars Data-> Radius: 0.53 x Earth's radius Mass: 0.11 x Earth's mass
Sojourner Data-> Mass of Sojourner vehicle: 11.5 kg, Wheel diameter: 0.13 m, Stored energy available: 5.4 x 10^5 J, Power required for driving under average conditions: 10 W, Land speed: 6.7 x 10^-3 m/s
Assume that when leaving the Pathfinder spacecraft Sojourner rolls down a ramp inclined at 20° to the horizontal. The ramp must be lightweight but strong enough to support Sojourner. Calculate the minimum normal force that must be supplied by the ramp
41N
A 42 kg wagon is being pushed with a metal rod that makes an angle of 46 degrees with the horizontal. The applied force is 449 N and the coefficient of kinetic friction between the wagon and the ground is 0.21. Find the acceleration of the wagon in the x-direction.
3.7 m/s^2
A curve with a radius of 50 m is banked at an angle of 25˚. The coefficient of static friction between the tires and the roadway is 0.3. . Find the correct speed of an automobile that does not require any friction force to prevent skidding.
15 m/s
What is the spring constant of a marble launcher that shoots a 0.0051 kg marble a height of 2.3 m above its muzzle assuming it is angled at 62° above the horizontal? The marble compressed the spring 0.080 m before being released.
47 N/m
A thin hoop (I = MR2) of mass 0.56 kg and radius 0.042 m rolls, without slipping, down an incline of height 0.67 m. What is the speed of the hoop at the bottom of the incline?
2.6 m/s
The design for a rotating spacecraft below consists of two rings. The outer ring with a radius of 30 m holds the living quarters and mimics the surface gravity of Earth, approximately 9.80 m/s2. The inner ring is designed to help the astronauts become accustomed to the surface gravity of a new planet: 7.35 m/s2. Calculate the spacecraft’s period of rotation.
*(Draw diagram)
T= 11 seconds