PHY 191
An irregularly shaped object 10m long is placed with each end on a scale. If the scale on the right reads 74N and the scale on the left reads 93N, how far from the left is the center of gravity
93x = 74(10-x)
an aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 35 seconds to complete the circle and the wingspan of the plane is 11 m, what is the acceleration of the wing tip?
ar = (r2π/T)²/r
A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?
use vf²=vi²+2a∆s, then vf=vi+a∆t
A ball is thrown at a 60-degree angle above the horizontal across level ground. It is thrown from a height of 2 meters above the ground with a speed of 22 m/s and experiences no appreciable air resistance. What is the time the ball remains in the air before striking the ground?
vf=vi+a∆t ∆y=vi*t+1/2a*t
A 1000-kg car is driving toward the north along a straight horizontal road at a speed of 20.0 m/s. The driver applies the breaks, and the car comes to a rest uniformly in a distance of 200m. What are the magnitude and direction of the net force applied to the car it brings it to rest?
vf²=vi²+2a∆s, find a ∑F =ma, find ∑F
On the earth, when an astronaut throws a 0.250kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity, and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is
vi=(mg/2)(2T)
The figure shows an acceleration vs force graph for three objects pulled by rubber bands. The mass of object 2 is 36 kg. What are the masses of objects 1 and 3?
∑F=ma, find a, compare to object 2
You walk 34 meters to the north, then turn 60 degrees to your right and walk another 45 meters. How far are you from where you originally started?
√(y+"x"cosθ)²+("x"sinθ)²
Two balls of clay of known masses hang from the ceiling on massless strings of equal lengths. They barely touch when both hang at rest. One ball is pulled back until its string is at 45 degrees, then released. It swings down, collides with the second ball, and they stick together. To determine the angle to which the balls swing on the opposite side, would you invoke: conservation of momentum, conservation of mechanical energy, both, either but not both, or these principles alone are not sufficient to find the angle?
Both
A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 5.00 m/s when it starts up a ramp that makes an angle of 25.0 degree with the horizontal. What is the speed of the sphere after it rolled 3.00 m up the ramp, measured along the surface of the ramp?
Ei = Ef =) ½mvi² + ½Iωi²=½mvf²+½Iωf²+mgy, use I = 2/5 mr² and ω = v/r, find vf
You swing a bat and hit a heavy box with a force 1500N. The force the box exerts on the bat is
Exactly 1500N whether or not the box moves
A 200-g hockey puck is launched up a metal ramp that is inclined at a 30 degree angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are µs = 0.40 and µk = 0.30, respectively. The puck's initial speed is 63 m/s. What vertical height does the puck reach above its starting point?
Ff + Fwsinθ = ma, find a vf²=vi²+2a∆x, find ∆x and multiple by sinθ
A car travels at a steady 40.0 m/s around a horizontal curve of radius 200m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding
Fk=Fr =) mgµ=mv²/gr, find µ
A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg*m2. If the arms are pulled in so the moment of inertia decreases to 1.80kg*m2, what is the final angular speed?
Li=Lf =) Iiωi = Ifωf, find ωf
A 95 N force exerted at the end of a 0.45m long torque wrench gives rise to a torque of 15Nm. What is the angle (assumed to be less than 90 degrees) between the wrench handle and the direction of the applied force?
T = rFsinθ, find θ
A string is attacked to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists all the forces directly acting on the ball
Tension and gravity
A ball is thrown directly upward and experiences no air resistance. What can be said about its acceleration
The acceleration is downward the entire time
A potential energy function for system 1 is given by U1(x) = Cx²+Bx³. The potential energy function for system 2 is given by U2(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?
The force is identical on the two systems
You are travelling in a vehicle at 50 m/s. A baseball is hit toward you at a 70 degree angle above the horizontal with a speed of 20 m/s relative to the Earth. What speed and direction do you measure for the ball
Vc + Vb*cosθ = velocity relative to car θ = arctan ((Vb*sinθ)/velocity relative to car)
In the figure, a constant external force P=160N is applied to a 20.0-kg box, which is on a rough horizontal surface. While the force pushes the box a distance of 8.00 m, the speed changes from 0.500 m/s to 2.60 m/s. The work done by friction during this process is closest to...
Wnet = KEf - KEi + Wext ½mvf²-½mvi² + Pcosθ*L
The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes it 0.90s to reach the floor. What is the mass m of the other block? The pulley has no appreciable mass or friction
a = (g(m2-m1))/(m2+m1), find m1
An object starts from rest at time t = 0s and moves in the +x direction with constant acceleration. The object travels 6.00 m from time t=1s to t=2s. What is the acceleration of the object
find acceleration at each x value
The position of an object is given by x=at^3-bt^2+ct where a = 4.1m/s^3, b=2.2 m/s^2, c=1.7 m/s, and x and t are in SI units. What is the instantaneous acceleration of the object when t=0.6s?
find second derivative and find t at 0.6
A baseball is thrown vertically upward and feels no air resistance. As it is rising...
its momentum is not conserved, but its mechanical energy is conserved
If an object travels at a constant speed in a circular path, the acceleration of the object is
larger in magnitude the smaller the radius of the circle
A brick is resting on a rough incline as shown in the figure. The friction force acting on the brick, along the incline, is
less than the weight of the block
A 480-kg car moving at 14.4 m/s hit from behind a 570-kg car moving at 13.3 m/s in the same direction. If the new speed of the heavier car is 14.0 m/s, what is the speed of the lighter car after the collision, assuming that any unbalanced forces on the system are negligibly small?
m1iv1i+m2iv2i-m2fv2f/m1f=v1f
Two ice skaters push off against one another starting from a stationary position. The 45.0-kg skater acquires a speed of 0.375 m/s. What speed does the 60.0-kg skater acquire? Assume that any other unbalanced forces during the collision are negligible
m1v1=m2v2, find v2
A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.
mg = (mv²)/r, find v
A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16m. What is the speed of the car at the top of the hill? Neglect any frictional effects.
mgyi = ½mv² + mgyf, find v
A car is heading north collides at an intersection with a truck of the same mass as the car heading east. If they lock together and travel at 28 m/s at 20 degrees north of east just after the collision, how fast was the car initially traveling? Assume that any other unbalanced forces are negligible.
vi=2vfsinθ
An object has a position given by r = [2m + (3m/s)t]i + [3m - (2m/s^2)t^2]j, where quantities are in SI units. What is the speed of the object at time t=2 seconds?
x = 2 +3t =) 3 3 y =3-2t^2 =) -4t -8 √3^2+8^2
A stalled car is being pushed up a hill at a constant velocity by three people. The net force on the car is
zero
A 600 kg car is going around a banked curve with a radius of 110 m at a speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction
θ = arctan (v²/gR)
A driver in a 1000-kg car traveling at 20 m/s slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the level road is 0.80, how long will the skid marks be?
∑F= ma =) mgµ=ma, find a vf²=vi²+2a∆x, find ∆x
A 60kg person rides in an elevator while standing on a scale. The scale reads 400N. The acceleration of the elevator is closest to
∑F=ma Fn-Fw=ma