KINEMATICS
The vertical and horizontal accelerations of a projectile
What is -9.8m/s2 and 0?
Explanation: In the y-direction, an object in a projectile accelerates with gravity. In the x-direction, there is no acceleration and stays at a constant velocity.
The force that propels a car forward is provided by the
road
It is the friction force that allows for the tires to move. Think of tires trying to move on ice - they cannot because there is no friction.
A box of mass m slides down a frictionless inclined plane of length L and vertical height h. What is the change in its gravitational potential energy?
-mgh
Since the forces are conservative, it is not the length that matters, but rather the height.
A football team's kicker punts the ball, mass = 0.4 kg, and gives it a launch speed of 30m/s. Find the impulse delivered to the football by the kicker's foot and the average force exerted by the kicker on the ball, given that the impact time is 8 milliseconds.
1500 N
Use that impulse is equal to linear momentum and that the average force is equal to impulse divided by time.
An infant crawls 5m east, then 3 m north, then 1 m east. Find the magnitude of the infant's displacement.
6.7m
Draw out a diagram where x = 6m and y =3m and use the Pythagorean Theorem to solve for the hypotenuse of the triangle, the displacement.
A person who weighs 800N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5m/s2, what will the scale read?
1200N
Draw out a free body diagram and write out your net force equation. You get FN+FW=ma and solve for FN since that is what shows up on the scale.
A force of 200 N is required to keep an object sliding at a constant speed of 2 m/s across a rough floor. how much power is being expended to maintain this motion?
400 W
Use the equation P=Fv.
An object of mass 2kg has a linear momentum of magnitude 6kg m/s. What is this object's kinetic energy?
9J
Get velocity using p=mv and then substitute it into KE=1/2mv2
An airplane drops a payload while traveling due north, parallel to the ground, at a constant speed of 100m/s. If air resistance is neglected, what is the velocity of the payload relative to the plane 4.0s after it is released?
40 m/s down
Explanation: Find the distance between the plane and payload and the velocity of the payload after 4s and then you can find the relative velocity.
The coefficient of static friction between a box and a ramp is 0.5. The ramp's incline angle is 30degrees. If the box is placed at rest on the ramp, the box will do what?
Accelerate down the ramp
The force pulling the block down the ramp is mgsinθ and the force of static friction is μmgcosθ. Since sinθ is greater than μcosθ, there is a net force and an acceleration down the ramp.
A box slides down an inclined plane at 37degrees. The mass of the block, m, is 35kg, the coefficient of kinetic friction between the box and the ramp is 0.3, and the length is 8m. How much work is done by gravity? How much work is done by the normal force?
Work done by gravity = 1690J
mgsinθ * d
Work done by normal = 0 J
Normal force is perpendicular to motion so the work done by this force is 0
A ball of mass m traveling horizontally with velocity v strikes a massive vertical wall and rebounds back along its original direction with no change in speed. What is the magnitude of the impulse delivered by the wall to the ball?
2mv
Impulse = change in momentum. Before it is mv and after it is -mv so the difference between the two is 2mv.
If an object is thrown straight upward with an initial speed of 8m/s and takes 3s to strike the ground, from what height was the object thrown?
21m
Write out givens and constants, like a=-10m/s2 and then plug into kinematics equations.
A 60cm rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is 3kg. At the lowest point in its path, the tension in the rope is 50N. What is the speed of the bucket?
2m/s
Draw out a free body diagram and net force equation to get FT-FW=mv2/r.
A car with mass of 800kg is traveling with an initial speed of 10m/s. When the brakes of the car are applied, the car starts to skid, and it experiences a frictional force with uk=0.2. What is the skidding distance of the car?
25m
Using Wf=∆KE and that θ=180, solve for d.
A wooden block of mass M is moving at speed V in a straight line. How fast would the bullet of mass m need to travel to stop the block assuming that the bullet became embedded inside?
MV/m
The linear momentum of the block and bullet need to be equal in magnitude since after impact it is zero.
An object is projected upward with a 30degree launch angle and an initial speed of 40m/s. How long will it take for the object to reach the top of its trajectory? How high is this?
2s, 20m
Remember to split up x and y components. To solve for the top of its trajectory, use that the y component of the velocity will equal zero at the top. Plug into kinematic equations.
v=(GM/r)1/2
Set Fgrav=Fc and solve for v.
80,000W
Use P=Fv and F=mv
Object 1 moves with an initial speed of v0 toward Object 2, which has a mass half that of Object 1. If the final speed of both objects after colliding is 0, what must have been the initial speed of Object 2 assuming no external forces?
2v0
Linear momentum is conserved. If the final speed of both objects is 0, that means total linear momentum after collision is zero which means total linear momentum before the collision is zero.